Factors of 336
Did you know that 336 is an even composite number whose prime factorization consists of three prime numbers, 2, 3, and 7? The sum of the prime factors of 336 is 12, which is again a composite number. In this chapter, we will calculate the factors of 336, the prime factors of 336, and the factors of 336 in pairs along with solved examples and interactive questions.
 Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
 Prime Factorization of 336: 336 = 2^{4} × 3 × 7
1.  What Are the Factors of 336? 
2.  How to Calculate the Factors of 336? 
3.  Factors of 336 by Prime Factorization 
4.  Factors of 336 in Pairs 
5.  FAQs on Factors of 336 
What Are the Factors of 336?
The factors of 336 are the numbers which on multiplication give 336. These are the numbers which divide 336 without leaving any remainder. Hence, when we multiply any two whole numbers with each other and obtain 336 as the answer, both the numbers are said to be the factors of 336.
How to Calculate the Factors of 336?
We can calculate the factors of 336 by finding all the numbers which divide 336 without leaving any remainder. Let's start by checking the factors of 336, starting from 1. We can express 336 as a product of its prime factors in the prime factorization method and we can divide 336 with its divisors in the division method. For the numbers dividing 336 entirely, the divisors as well as their quotients are the factors of 336.
Numbers dividing 336  Factors of 336 

336/1 = 336  1 and 336 are factors of 336 
336/2 = 168  2 and 168 are factors of 336 
336/3 = 112  3 and 112 are factors of 336 
336/4 = 84  4 and 84 are factors of 336 
336/6 = 56  6 and 56 are factors of 336 
336/7 = 48  7 and 48 are factors of 336 
336/8 = 42  8 and 42 are factors of 336 
336/12 = 28  12 and 28 are factors of 336 
336/14 = 24  14 and 24 are factors of 336 
336/16 = 21  16 and 21 are factors of 336 
Hence, the factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168 and 336.
Explore factors using illustrations and interactive examples.
 Factors of 168  The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
 Factors of 112  The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112.
 Factors of 84  The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
 Factors of 42  The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
 Factors of 21  The factors of 21 are 1, 3, 7, and 21.
Factors of 336 by Prime Factorization
When a composite number is expressed as the product of its prime factors, it is called as prime factorization. To get the prime factorization of 336, we use two methods:
 Method 1: Factor Tree Method
 Method 2: Upside Down Division Method
Method 1: Factor Tree Method
Factor tree of 336 is:
Method 2: Upside Division Method
We divide 336 by its smallest prime factor which is 2
336/2 = 168
168 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1. Thus, the prime factorization of 336 is:
Hence, the prime factors of 336 are 2, 3, and 7.
The prime factorization of 336 is 2^{4} × 3 × 7.
Factors of 336 in Pairs
The pair of numbers which on multiplication give 336 are the factor pairs of 336. Let's observe the following factors of 336 in pairs. The negative pair factors of 336 are obtained when the product of two negative numbers is taken (  ve ×  ve ) = +ve.
 Positive Pair Factors of 336 are: (1, 336), (2, 168), (3, 112), (4, 84), (6, 56), (7, 48), (8, 42), (12, 28), (14, 24), (16, 21)
 Negative Pair Factors of 336 are: (1, 336), (2, 168), (3, 112), (4, 84), (6, 56), (7, 48), (8, 42), (12, 28), (14, 24), (16, 21)
Important Notes:
 As 336 ends with its last two digits as 36 and 36 is divisible by 4, we can say that 4 is one of the factors of 336.
 As the sum of the digits of 336 is 12, one of the factors of 336 is 3.
 336 is a nonperfect square number. Hence, it has even number of factors.
Challenging Questions:
 Are 672 and 3/4 factors of 336? Why do you think so?
Factors of 336 Solved Examples

Example 1: Andy has to find the common factors of 336 and 625. Help him find them.
Solution:
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
The factors of 625 are 1, 5, 25, 125, and 625.
Hence, the common factor of 336 and 625 is 1. 
Example 2: Can a rectangular box of length 16 inches and breadth 15 inches fit inside a rectangular box of area 336 square inches?
Solution:
The area of the given rectangular box of length 16 inches and breadth 15 inches is, area = 16 × 15 = 240 square inches while the area of other box is of 336 square inches.
The area of rectangular box of length 16 inches and breadth 15 inches is 240 square inches, which is less than the area of the other rectangular box of 336 square inches.
Hence, the rectangular box of length 16 inches and breadth 15 inches can fit inside the rectangular box of area 336 square inches.
FAQs on Factors of 336
What are the factors of 336?
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
What are the prime factors of 336?
The prime factors of 336 are 2, 3, and 7.
Are all the factors of 336 prime?
No, all the factors of 336 are not prime.
What are the common factors of 336 and 440?
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220 and 440.
Hence, the common factors of 336 and 440 are 1, 2, 4 and 8.
Is 9 a factor of 336?
No, 9 is not a factor of 336.
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