3Digit Multiplication
3digit multiplication in mathematics is a process of multiplying 3digit numbers by 2digit numbers, 1digit numbers, or 3digit numbers by placing numbers in columns according to their place values. Threedigit multiplication goes a step ahead if it is compared to 2digit or 1digit multiplication.
In this article, we will learn 3digit by 1digit multiplication, 3digit by 2digit multiplication, and 3digit by 3digit multiplication and solve a few examples for a better understanding of the concept.
1.  What is 3Digit Multiplication? 
2.  3Digit By 1Digit Multiplication 
3.  3Digit By 2Digit Multiplication 
4.  3Digit By 3Digit Multiplication 
5.  FAQs on 3Digit Multiplication 
What is 3Digit Multiplication?
3digit multiplication is a method of multiplying 3digit numbers with other numbers. When we multiply threedigit numbers, we arrange the numbers in columns according to the place values of the digits. We know that 3digit numbers are arranged as per their place values as ones, tens, and hundreds. Once we have a set of two numbers to multiply, we usually keep the larger number on top and the smaller number below it. The number that is placed on top becomes the multiplicand and the number written below is the multiplier. When numbers are arranged according to their place values, we multiply the multiplier with all the digits of the multiplicand one by one starting from the ones digit, followed by the tens digit, and then the hundreds digit. All these products are written together and they result in the final product.
For example, if we need to multiply 123 × 3, we place them as shown below where 123 is the multiplicand and 3 is the multiplier. After multiplying these numbers we get the product as 269
Let us now learn how to do 3digit multiplication with different numbers.
3Digit By 1Digit Multiplication
When a 3digit number is multiplied by a 1digit number, we have two scenarios.
 The first one refers to the multiplication in which the 1digit number is simply multiplied by the 3digit number without any carryovers and we get the product. This is 3digit multiplication without regrouping.
 The second one refers to the multiplication in which we multiply the 3digit number with a 1digit number and we need to carry over the extra digit of the product to the next column. This is 3digit multiplication with regrouping. Let us discuss both the cases with the help of examples.
3Digit Multiplication Without Regrouping
In order to find the product of a 3digit number and a 1digit number, we multiply the 1digit number by each digit of the 3digit number. If the product of the 1digit number with each digit of the number is a single digit, then there is no need for carrying over any number. Let us consider an example.
Example: Multiply 214 × 2
Solution: The following steps show the procedure of multiplying 214 by 2.
 Step 1: Arrange the numbers 214 and 2 in columns according to their place values as shown in the figure given below.
 Step 2: Now, first we multiply the 1digit number (2) by each digit of the 3digit number (214)
 When 2 is multiplied by 4, we get 8.
 When 2 is multiplied by 1, we get 2.
 When 2 is multiplied by 2, we get 4.
 Step 3: Therefore, the product that we get is 428.
3 Digit Multiplication With Regrouping
In this section, we will multiply a 3digit number by a 1digit number and see how regrouping works. Let us solve an example to demonstrate this.
Example: Multiply 347 by 3.
Solution: Let us multiply 347 by 3 using the steps given below.
 Step 1: Arrange the numbers 347 and 3 in columns according to their place values as shown below.
 Step 2: Multiply 3 by each digit of 347.
 When 3 is multiplied by 7, we get 21. Since 21 is a 2digit number, we write 1 under the ones column and carry 2 to the tens column above 4.
 When 3 is multiplied by 4, we get 12. Now, we need to add the carryover (2) to 12 and we get 14. Since 14 is a 2digit number, we write 4 under the tens column and carry 1 to the hundreds column above 3.
 When 3 is multiplied by 3, we get 9. Now, we need to add the carryover 1 to 9 and we get 10. Since there is no other digit left for multiplication, we write 10.
 Step 3: Therefore, we get the product as 1041.
3Digit by 2Digit Multiplication
In order to multiply 3digit numbers by 2digit numbers, we first write the 3digit number on top and the 2digit number below it. Let us discuss the 3digit by 2digit multiplication without regrouping and with regrouping in the following sections.
3Digit by 2Digit Multiplication Without Regrouping
When we multiply a 3digit number by a 2digit number, we multiply the ones digit of the multiplier with the multiplicand, then we multiply the tens digit of the multiplier with the multiplicand. Then we add both these products to get the final product. Let us discuss the process stepbystep with the help of the following example.
Example: Multiply 411 by 31.
Solution: Let us multiply 411 by 31 stepwise.
 Step 1: Arrange the numbers 411 and 31 in columns according to their place values as shown below.
 Step 2: Multiply 1 by each digit of 411.
 When 1 is multiplied by 1, we get 1.
 When 1 is multiplied by 1, we get 1.
 When 1 is multiplied by 4, we get 4. So, we have 411 as the first partial product.
 Step 3: Now, we place a zero under the first partial product, that is, just before we write the second partial product in the next line. This 0 is placed here because in this step we are actually multiplying 411 by 30.
 Step 4: Multiply 3 by each digit of 411.
 When 3 is multiplied by 1, we get 3.
 When 3 is multiplied by 1, we get 3.
 When 3 is multiplied by 4, we get 12. So, we have 12330 as the second partial product.
 Step 5: Add these products to obtain the final answer.
 Step 6: 411 + 12330 = 12741. Therefore, the final product is 12741.
3Digit by 2Digit Multiplication With Regrouping
Now that we have multiplied a 3digit number by a 2digit number, let us try solving another problem involving regrouping or carrying.
Example: Multiply 573 by 46.
Solution: Let us multiply 573 by 46 using the following steps:
 Step 1: Arrange the numbers 573 and 46 in columns according to their place values as shown below.
 Step 2: Multiply 6 by each digit of 573.
 When 6 is multiplied by 3, we get 18. Since 18 is a 2digit number, we write 8 under the ones column and carry 1 to the tens column above 7.
 When 6 is multiplied by 7, we get 42. Now, we need to add the carryover (1) to 42 and we get 43. Since 43 is a 2digit number, we write 3 in the tens column and carry 4 to the hundreds column above 5.
 When 6 is multiplied by 5, we get 30. Now, we will add the carryover (4) to 30, we get 34. Since there is no other digit left for multiplication, we write 34. So, we have 3438 in the first line (partial product) of the answer.
 Step 3: Now, we will place a zero under the first partial product, that is, before writing the second partial product in the next line. This is because in this step we are actually multiplying 573 with 40.
 Step 4: Multiply 4 by each digit of 573.
 When 4 is multiplied by 3, we get 12. Since 12 is a 2digit number, we write 2 under the tens column and carry 1 to the tens column above 7.
 When 4 is multiplied by 7, we get 28. Now, we will add the carryover 1 to 28 to get 29. Since 29 is a 2digit number, we write 9 under the hundreds column and carry 2 to the hundreds column above 5.
 When 4 is multiplied by 5, we get 20. Now, we will add the carriedover number 2 to 20 and we get 22. Since there is no other digit left for multiplication, we write 22. So, we have 22920 as the second line of the product.
 Step 5: Add these partial products to obtain the final answer.
 Step 6: This means 3438 + 22920 = 26358. Therefore, the final product is 26358.
3Digit By 3Digit Multiplication
In this section, we will learn how to multiply a 3digit number by a 3digit number. This process is similar to what we discussed in the previous sections. Let us understand 3digit by 3digit multiplication with the help of the following example.
Example: Multiply 123 by 456.
Solution: Let us multiply 123 by 456 using the following steps.
 Step 1: Arrange the numbers 123 and 456 in columns according to their place values as shown below.
 Step 2: Multiply 6 by each digit of 123.
 When 6 is multiplied by 3, we get 18. Since 18 is a 2digit number, we write 8 under ones column and carry 1 to the tens column above 2.
 When 6 is multiplied by 2, we get 12. Now, we add the carriedover 1 to 12 and we get 13. Since 13 is a 2digit number, we write 3 under the tens column and carry 1 to the next column above 1.
 When 6 is multiplied by 1, we get 6. Now, add the carriedover 1 to 6 to get 7. Since there is no other digit left for multiplication, we write 7. So, we have 738 in the first line as the partial product.
 Step 3: Now, place a zero under this partial product under ones column. This is because in this step we are actually multiplying 123 with 50.
 Step 4: Multiply 5 by each digit of 123.
 When 5 is multiplied by 3, we get 15. Since 15 is a 2digit number, we write 5 in the tens column and carry 1 to the next column above 2.
 When 5 is multiplied by 2, we get 10. Now, add the carriedover 1 to 10 to get 11. Since 11 is a 2digit number, we write 1 in hundreds column and carry 1 to the next column above 1.
 When 5 is multiplied by 1, we get 5. Now, add the carriedover 1 to 5 to get 6. Since there is no other digit left for multiplication, we write 6. So, we have 6150 in the second line of the partial product.
 Step 5: Now, place two zeros (0s) under the ones and tens column under the partial product obtained in the previous step. This is because in this step we are actually multiplying 123 with 400.
 Step 6: Multiply 4 by each digit of 123.
 When 4 is multiplied by 3, we get 12. Since 12 is a 2digit number, we write 2 under the hundreds column and carry 1 to the next column above 2.
 When 4 is multiplied by 2, we get 8. Now, add the carriedover 1 to 8 to get 9. We write 9 under the next column.
 When 4 is multiplied by 1, we get 4. Since there is no other digit left for multiplication, we write 4. So, we have 49200 in the third line as the partial product.
 Step 7: Add all the 3 partial products to obtain the final product. This means 738 + 6150 + 49200 = 56088.
 Step 8: Therefore, the final product is 56088.
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3Digit Multiplication Examples

Example 1: Multiply 341 and 4.
Solution: To multiply the given numbers 341 and 4, we will arrange them in columns. Multiply 4 by each digit of 341 to obtain the product.
Answer: The product of 341 and 4 is 1364.

Example 2: Find the product of 712 and 23.
Solution: Let us do this 3digit multiplication using the following steps.
 Multiply 3 by each digit of 712.
 Place a zero on ones place below the product obtained above.
 Multiply 2 by each digit of 712.
 Add the two products to obtain the final answer.
Answer: The product of 712 and 23 is 16376.

Example 3: State true or false with respect to 3digit multiplication.
a.) 324 × 100 = 32400
b.) 414 × 10 = 41400
Solution:
a.) True, 324 × 100 = 32400
b.) False, 414 × 10 = 4140
FAQs on 3Digit Multiplication
What is 3Digit Multiplication?
3digit multiplication in mathematics is a process of multiplying 3digit numbers by 1digit numbers, 2digit numbers, and 3digit numbers by placing the numbers in columns according to their place values.
How to do 3Digit Multiplication?
3digit multiplication can be done easily if the numbers are arranged according to their place values. Once we have a set of two numbers to multiply, we usually keep the larger number on top and the smaller number below it. The number that is placed on top becomes the multiplicand and the number written below is the multiplier. When numbers are arranged according to their place values, we multiply the multiplier with all the digits of the multiplicand one by one starting from the ones digit, followed by the tens digit, and then the hundreds digit. All these products are written together and they result in the final product.
How to do 3Digit by 1Digit Multiplication?
To multiply a 3digit number by a 1digit number, we multiply the 1digit number by each digit of the 3digit number to get the product. For example, let us multiply 314 × 2. We multiply 2 with 4 to get 8 which will be placed under the ones column. Then, we will multiply 2 with 1 to get 2 which will be placed under the tens column. After this, we will multiply 2 with 3 to get 6. Therefore, the product of 314 × 2 = 628.
What is 3Digit by 2Digit Multiplication?
When a 3digit number is multiplied by a 2digit number, we multiply each digit of the 2digit number by each digit of the 3digit number. We arrange the numbers in columns according to their place values, write the partial products one below the other and add them to get the final product.
What is 3Digit by 3Digit Multiplication?
3digit by 3digit multiplication means when a 3digit number is multiplied with another 3digit number. It is done by placing the numbers columnwise and then multiplying each digit of one number by each digit of the other number. The partial products are written one below the other and then the products are added to get the final answer.
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