Factors of 68
Factors of 68 are the numbers which when multiplied in pairs give the product as 68. These factors can be negative as well. The number 68 can be expressed as a sum of two prime numbers in two different ways. In this lesson, we will calculate the factors of 68, prime factors of 68, and factors of 68 in pairs along with solved examples for a better understanding.
 Factors of 68: 1, 2, 4, 17, 34, and 68
 Prime Factorization of 68: 68 = 2^{2} × 17
What are the Factors of 68?
Before we study about factors of 68, let's have a quick recall about "Factor". The number of factors is based on the type of number. A prime number is a number that consists of only two factors. A composite number is a number that has more than two factors. Coming back to number 68. Factors of 68 are 1, 2, 4, 17, 34, and 68. Therefore, 68 is a composite number.
How to Calculate the Factors of 68?
To calculate the factors of 68, start with the smallest whole number 1. Divide 68 with the number 1. Is the remainder zero? Yes! By factor definition, the number is divided equally without leaving a remainder.
 68 ÷ 1 = 68
 68 × 1 = 68
We try with the next whole number 2. Is the remainder zero? Yes!
 68 ÷ 2 = 34
 34 × 2 = 68
Proceeding in a similar manner we get,
 68 ÷ 4 = 17
 4 × 17 = 68
Thus, we calculated the factors of 68
Important Notes:
 Factors of 68 are 1, 2, 4, 17, 34, and 68
 Decimals and fractions are not considered as factors
 The number 68 is an even composite number
Explore factors using illustrations and interactive examples
 Factors of 38  The factors of 38 are 1, 2, 19, 38
 Factors of 42  The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
 Factors of 81 The factors of 81 are 1, 3, 9, 27, 81
 Factors of 48  The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
 Factors of 168  The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
 Factors of 180  The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Prime factorization is a process of breaking down the composite number into its prime factors. To get the prime factorization of 68, we divide it by its smallest prime factor, which is 268 ÷ 2 = 34. Now 34 is divided by its smallest prime number 2.
 34 ÷ 2 = 17
The process of prime factorization continues till we get the quotient as 1. Therefore, factors of 68 by prime factorization are:
It can also be written as 68 = 2 × 2 × 17
Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not? And as you might have already guessed, for prime numbers, there are no other factors.
Factors of 68 in Pairs
The pair of numbers which gives 68 when multiplied is called pair factors of 68. Factors of 68 in pairs are (1,68), (2,34), and (4,17)
Factors of 68 can have negative pair factors as well. We know () × () = +. Hence the negative pair factors of 68 are (1,68), (2,34), and (4,17).
Challenging Questions:
 Can 0.17 be a factor of 68?
 Can the factor of a number be greater than the number itself?
Factors of 68 Solved Examples

Example 1: What will be the sum of all the factors of 68?
Solution:
We know that the factors of 68 = 1, 2, 4, 17, 34, and 68
Thus,
The sum of the factors = 1 + 2 + 4 + 17 + 34 + 68 = 123
Hence, the sum of all factors of 68 is 123 
Example 2: Help Andrea list out the factor pairs of 68.
Solution:
 68 = 1 × 68
 68 = 2 × 34
 68 = 4 × 17
The Factors of 68 in pairs are (1,68), (2,34), and (4,17)
FAQs on Factors of 68
What are the factors of 68?
The factors of 68 are 1, 2, 4, 17, 34, and 68
What is the highest factor of 68?
68 is the highest factor of 18. Every number is the highest factor of itself.
Is 68 prime or composite?
The number 68 is composite since it has more than two factors.
What are all the common factors of 68 and 78?
The factors of 68 are 1, 2, 4, 17, 34, and 68.
The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78
Hence the common factors are 1, and 2
What are the common factors of 68 and 84?
The factors of 68 are 1, 2, 4, 17, 34, and 68
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Hence the common factors are 1, 2, and 4
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