3 Digit Multiplication

3 digit multiplication in mathematics is a process of multiplying 3 digit numbers by 2 digit numbers, 1 digit numbers, and 3 digit numbers by placing numbers in columns according to their place values. Three-digit multiplication is a little complex as compared to 2 digits and 1 digit multiplication. The numbers in 3 digit multiplication start from the hundred's place value, then comes the ten's place value and the last one is the unit's place value.

In this article, we will learn the process of 3 digit multiplication stepwise. We will discuss how to multiply 3 digit numbers with 3 digit numbers, 2 digit numbers, and 1 digit numbers. We will solve a few examples for a better understanding of the concept.

3 digit multiplication is a method of multiplying 3 digit numbers in mathematics. When we multiply three-digit numbers, we arrange the numbers in columns according to the place values of the digits. For 3 digit numbers, we arrange numbers stating from hundred, ten's, and units place. When numbers are arranged according to their place values, we multiply the other number with the digit at the units place of the 3 digit number, then we multiply the number with the digit at the tens place, and in the last, with the digit at the hundreds place.

For example, when 123 is multiplied by 12, we get the product equal to 1476. Let us now learn to 3 digit multiplication with different numbers.

When a 3 digit number is multiplied by a 1 digit number, we get two cases. One where the 1 digit number is simply multiplied by the 3 digit number without carrying and we get the product. Another, where when we multiply 3 digit number with the 1 digit number with carrying. Let us discuss both cases with the help of an example.

3 Digit Multiplication by 1 Digit Without Carrying

3 digit multiplication with a 1 digit is done by multiplying the 1 digit number by each digit of the 3 digit number. If the product of the 1 digit number with each digit of the number is a single digit, then there is no need for carrying. Let us consider an example.

Example: Show the 3 digit multiplication of 214 by 2.

Solution: Now, we will learn to multiply 214 by 2 stepwise.

• Step 1: Arrange the numbers 214 and 2 in columns according to their places values as shown in the image. We place the number with more digits first, then the number with a lesser number of digits below it.
• Step 2: Now, first we multiply the 1 digit number 2 by each digit of the 2 digit number.
  • 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: We have product 428 as our final answer.

3 Digit Multiplication by 1 Digit With Carrying

In this section, we will multiply a 3 digit number by a 1 digit number with carrying. Let us solve an example to demonstrate this.

Example: Multiply 347 by 3.

Solution: Now, we will multiply 347 by 3 stepwise.

• Step 1: Arrange the numbers 347 and 3 in columns according to their places values as shown in the image.
• Step 2: Multiply 3 by each digit of 347.
  • When 3 is multiplied by 7, we get 21. Since 21 is a 2 digit number, we write 1 at the unit's place and carry 2 above 4.
  • When 3 is multiplied by 4, we get 12. Now, add the carried 2 to 12, we get 14. Since 14 is a 2 digit number, we write 4 at the ten's place and carry 1 above 3.
  • When 3 is multiplied by 3, we get 9. Now, add the carried 1 to 9, we get 10. Since there is no other digit left for multiplication, we write 10.
• Step 3: We have the product equal to 1041.

In this section, we will learn 3 digit multiplication by 2 digit numbers. We first write the 3 digit numbers and the two-digit number below it according to the corresponding place values. As discussed above, we have two cases hee - one with carrying and another without carrying. Let us discuss the two cases with the help of an example.

3 Digit Multiplication by 2 Digit Without Carrying

In a 3 digit by 2 Digit multiplication, we multiply the digit at the unit's place of the 2 digit number by the 3 digit number, and then the digit at ten's place by the 3 digit number. Let us discuss the process step by step:

Example: Multiply 411 by 31.

Solution: Now, we will multiply 411 by 31 stepwise.

• Step 1: Arrange the numbers 411 and 31 in columns according to their places values as shown in the image.
• 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 in the first line of the answer.
• Step 3: Now, place a zero under the result obtained at the unit's place. This helps in blocking the space at the unit's position to proceed multiplication with tens place. This step is important.
• 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 in the second line of the answer.
• Step 5: Add the results obtained in step 2 and step 4 to obtain the final answer.
• Step 6: 411 + 12330 = 12741. Now, the final answer is 12741.

3 Digit Multiplication by 2 Digit With Carrying

Now that we have multiplied a 3 digit number by 2 digit number, let us try solving another problem where carrying is involved.

Example: Multiply 573 by 46.

Solution: To multiply 573 by 46, we follow the steps given below:

• Step 1: Arrange the numbers 573 and 46 in columns according to their places values as shown in the image.
• Step 2: Multiply 6 by each digit of 573.
  • When 6 is multiplied by 3, we get 18. Since 18 is a 2 digit number, we write 8 at the unit's place and carry 1 above 7.
  • When 6 is multiplied by 7, we get 42. Now, add the carried 1 to 42, we get 43. Since 43 is a 2 digit number, we write 3 at the ten's place and carry 4 above 5.
  • When 6 is multiplied by 5, we get 30. Now, add the carried 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 of the answer.
• Step 3: Now, place a zero under the result obtained at the unit's place. This helps in blocking the space at the unit's position to proceed multiplication with tens place. This step is important.
• Step 4: Multiply 4 by each digit of 573.
  • When 4 is multiplied by 3, we get 12. Since 12 is a 2 digit number, we write 2 at the ten's place and carry 1 above 7.
  • When 4 is multiplied by 7, we get 28. Now, add the carried 1 to 28, we get 29. Since 29 is a 2 digit number, we write 9 at the hundred's place and carry 2 above 5.
  • When 4 is multiplied by 5, we get 20. Now, add the carried 2 to 20, we get 22. Since there is no other digit left for multiplication, we write 22. So, we have 22920 in the second line of the answer.
• Step 5: Add the results obtained in step 2 and step 4 to obtain the final answer.
• Step 6: 3438 + 22920 = 26358. Now, the final answer is 26358.

In this section, we will now learn to multiply 3 digit numbers by a 3 digit number. This process is similar to what we discussed in the previous sections. We will solve an example to understand the 3 digit multiplication by a 3 digit number.

Example: Multiply 123 by 456.

Solution: To multiply 123 by 456, we follow the steps given below:

• Step 1: Arrange the numbers 123 and 456 in columns according to their places values as shown in the image.
• Step 2: Multiply 6 by each digit of 123.
  • When 6 is multiplied by 3, we get 18. Since 18 is a 2 digit number, we write 8 at the unit's place and carry 1 above 2.
  • When 6 is multiplied by 2, we get 12. Now, add the carried 1 to 12, we get 13. Since 13 is a 2 digit number, we write 3 at the ten's place and carry 1 above 1.
  • When 6 is multiplied by 1, we get 6. Now, add the carried 1 to 6, we get 7. Since there is no other digit left for multiplication, we write 7. So, we have 738 in the first line of the answer.
• Step 3: Now, place a zero under the result obtained at the unit's place. This helps in blocking the space at the unit's position to proceed multiplication with tens place. This step is important.
• Step 4: Multiply 5 by each digit of 123.
  • When 5 is multiplied by 3, we get 15. Since 15 is a 2 digit number, we write 5 at the ten's place and carry 1 above 2.
  • When 5 is multiplied by 2, we get 10. Now, add the carried 1 to 10, we get 11. Since 11 is a 2 digit number, we write 1 at the hundred's place and carry 1 above 1.
  • When 5 is multiplied by 1, we get 5. Now, add the carried 1 to 5, we get 6. Since there is no other digit left for multiplication, we write 6. So, we have 6150 in the second line of the answer.
• Step 5: Now, place two 0s under the result obtained at the unit's and ten's place. This helps in blocking the space at the unit's and ten's position to proceed multiplication with hundred's place. This step is important.
• Step 6: Multiply 4 by each digit of 123.
  • When 4 is multiplied by 3, we get 12. Since 12 is a 2 digit number, we write 2 at the hundred's place and carry 1 above 2.
  • When 4 is multiplied by 2, we get 8. Now, add the carried 1 to 8, we get 9. We write 9 at the thousand's place.
  • 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 of the answer.
• Step 7: Add the results obtained in step 2, step 4, and step 6 to obtain the final answer.
• Step 8: 738 + 6150 + 49200 = 56088. Now, the final answer is 56088.

Important Notes on 3 Digit Multiplication

• 3 digit multiplication in mathematics is a process of multiplying 3 digit numbers by 2 digit numbers, 1 digit numbers, and 3 digit numbers.
• For 3 digit numbers, we arrange numbers stating from hundred, ten's, and units place.

☛ Related Articles:

• Subtraction
• Division
• Multiplication and Division of Integers

What is 3 Digit Multiplication?

3 digit multiplication in mathematics is a process of multiplying 3 digit numbers by 2 digit numbers, 1 digit numbers, and 3 digit numbers by placing numbers in columns

How to Multiply 3 Digit by 1 Digit?

To multiply a 3 digit number by 1 digit number, we multiply the 1 digit number by each digit of the 3 digit number.

What is 3 Digit by 2 Digit Multiplication?

When a 3 digit number is multiplied by a 2 digit number, we multiply each digit of the 2 digit number by each digit of the 3 digit number. We arrange the numbers in columns according to their place values.

How Do You Do 3 Digit Multiplication?

When we multiply three-digit numbers, we arrange the numbers in columns according to the place values of the digits. For 3 digit numbers, we arrange numbers stating from hundred, ten's, and units place.

How to Do 3 Digit by 3 Digit Multiplication?

3 Digit by 3 Digit Multiplication is done by placing the numbers column-wise and then multiply each digit of one number by each digit of the other number.