Factors of 294
12 Factors of 294 are discussed in this minilesson. The product of factors of 294 when multiplied in pairs gives 294. On dividing 294 by its factors we get remainder as zero. It is an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 294, prime factors of 294, and factors of 294 in pairs along with solved examples for a better understanding.
 Factors of 294: 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147 and 294.
 Prime Factorization of 294: 294 = 2 × 3 × 7 × 7.
1.  What Are the Factors of 294? 
2.  How to Calculate Factors of 294? 
3.  Important Notes 
4.  Factors of 294 by Prime Factorization 
5.  Factors of 294 in Pairs 
6.  Tips and Tricks 
7.  FAQs on Factors of 294 
What Are Factors of 294?
The factors of 294 are those numbers that divide it completely without leaving any remainder. They multiply together to give the product 294. 294 is a composite number and it has 12 factors. The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147 and 294.
How to Calculate the Factors of 294?
Factors of the number 294 can be calculated as follows:

Write the smallest factor of 294 (except for 1). The smallest factor of 294 is 2, 294 ÷ 2 = 147. So, 2 and 147 are the factors of 294.

Write the next smallest factor of 3. 294 ÷ 3 = 98. So, 3 and 98 are the factors of 294

Now proceed until you reach 147(half of 270)
Thus we can verify that there are 12 integers that are factors of 294
Divisibility test  Factor of 294 

294 ÷ 1 = 294  (1,294) 
294 ÷ 2=147  (2,147) 
294 ÷ 3=98  (3,98) 
294 ÷ 6 = 49  (6,49) 
294 ÷ 7=42  (7,42) 
294 ÷ 14=21  (14,21) 
Important Notes
 Composite numbers have more than 2 factors, and 294 is a composite number.
 Prime numbers have only 2 factors, 1 and the number itself.
Factors of 294 by Prime Factorization
 Write down the number to be factored, which is 294
 Start dividing it with the prime factor 2, 294÷2=147.
 3 is the next prime factor, 147÷3=49.
 Break 49 into its factors. 49 is a perfect square. 7 × 7= 49. 7 is a prime number.
We stop here as we have found all the prime factors of 294. Thus, the prime factorization is 2 × 3 × 7 × 7.
What Are the Pair Factors of 294?
Any two sets of numbers that pair up to form the number 294 are its factor pairs. The following are the factors of 294 in pairs.
Here are the 6 positive factors of 294 in pairs are (1,294), (2,147), (3,98), (6,49), (7,42), and (14,21).
Here are the 6 negative factors of 294 in pairs are (1,294), (2,147), (3,98), (6,49), (7,42), and (14,21).
Tips and Tricks
 Start dividing the composite numbers until the quotient is a prime number
 Every number has a minimum of 2 factors, i.e., 1 and the number itself
 Using the divisibility tests, we can find the factors easily
 Get the prime factorization done for the composite numbers. Express them in exponential form.
Solved Examples on Factors of 294

Example 1 : Joanne is given several cards. They are numbered 42, 48, 97, 147. Her teacher has asked her to pick the numbers that are the factors of 294. Can you help her out?
Solution:
A number is a factor only if it divides 294 completely without any remainder.
Divide 294 by all the numbers one by one. 294÷42=7, Remainder =0
 294÷48=6, Remainder = 6
 294÷97=3, Remainder = 3
 294÷147=2, Remainder = 0
 42 and 147 divide 294 completely without any remainder.

Example 2 Henry sets up a grocery stall. He has 42 apples, 49 oranges and 21 mangoes. He wishes to arrange the apples, oranges, and mangoes in 7 rows equally. Can you help him arrange the fruits?.
Solution:
Henry needs to arrange the fruits in 7 rows.
He knows one factor of all the three given numbers, which is 7
So, he needs to divide each of the numbers by 7, to find the other factor.
42 apples in 7 rows = 42÷7=6
which means 6 apples will be arranged in each of the 7 rows.
49 oranges in 7 rows= 49÷7=7
which means 7 oranges will be arranged in each of the 7 rows.
21 mangoes in 7 rows= 21÷7=3
which means 3 mangoes will be arranged in each of the 7 rows.
Hence, Henry should arrange 6 apples in 7 rows,7 oranges in 7 rows, 3 mangoes in 7 rows.
FAQs on Factors of 294
1.Which factor of 294 is a perfect square?
49 is a perfect square factor of 294
2. What are the factors of 294 that add up to 35?
The factors of 294 are 1, 2, 3, 6, 7,14, 21, 42, 49, 98, 147, 294.
Among these 12 factors, 14 and 21 sums to 35.
3. What are the prime factors of 294?
The prime factors of 294 are 2, 3, 7, 7.
4. Is 294 a perfect square?
294 is not a perfect square.
5. What is the highest common factor of 294 and 84?
The highest common factor of 294 and 84 is 42.
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