Factors of 68 Using Prime Factorization
What are the Factors of 68?
Factors of 68 are those natural numbers that divide 68 without leaving any remainder. We can also say that factors of 68 will divide it evenly. Factors of 68 can be positive as well as negative but they cannot be decimal numbers or fractions. The quotient obtained on dividing 68 by its factor is also a factor of 68.
Factors of 68
Factor List for Number 68
We can stop after checking for 4 because the factor pairs start to repeat.
Hence the factors of 68 are 1, 2, 4, 17, 34 and 68.
[Note: If we divide 68 by 10, we get the quotient and remainder as 6 and 8, respectively. This means the remainder is not zero. So 10 is not a factor of 68.]
Prime Factors of 68
A factor tree can be used to determine the prime factors of 68 as shown in the figure.
From the factor tree we can see prime factorization of 68 is 2 \(\times\) 2 \(\times\) 17 = \(2^2 \times\) 17.
This means 2 and 17 are the prime factors of 68.
Factor Pairs of 68
The factor pair of any number is a set of its two factors which when multiplied result in that number. A factor pair can be negative or positive.
[Note: Product of two negative numbers is positive.]
The factor pair of 68 is the set of two factors of 68 which when multiplied results in 68 as the product.
Thus the factor pairs of 68 can be obtained from the list of its factors.
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Rapid Recall
Solved Factors of 68 Examples
Example 1: 68 brownies are distributed evenly among a group of 17 children. Find out the number of brownies each child will get.
Solution:
Number of children = 17
Number of brownies = 68
Since 17 is a factor of 68, the brownies can be divided into equal shares without cutting them into smaller pieces.
Dividing 68 by 17
68 \(\div\) 17 = 4
Hence, each child will get 4 Brownies.
Example 2: What are the common factors of 68 and 18?
Solution:
Factors of 68 are 1, 2, 4, 17, 34 and 68
Factors of 18 are 1, 2, 3, 6, 9, and 18.
So, the common factors of 68 and 18 are 1 and 2.
Example 3: Find out the common factors of 68 and 72.
Solution:
Factors of 68 are 1, 2, 4, 17, 34, 68.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Therefore, the common factors of 68 and 72 are 1, 2 and 4.
Prime factorisation of 68 is \(2^2 \times 17\)
So, prime factors of 68 are 2 and 17.
Yes, 68 is a composite number as it has factors other than 1 and itself, that is, 68. In other words the number 68 has more than two factors. It has factors 2, 4, 17, 34 other than 1 and 68.
The factors of 68 are 1, 2, 4, 17, 34 and 68.
So, the least factor of 68 is 1 and the greatest factor is 68 itself.
The factors of 68 are 1, 2, 4, 17, 34 and 68.
The sum of the all the factors of 68 is
= 1 + 2 + 4 + 17 + 34 + 68 = 126
Hence, the sum is 126.
Factors of 68 are 1, 2, 4, 17, 34 and 68.
So, the number 68 has 6 factors.