Factors of 64 Using Prime Factorization
Factors of 64
What are the Factors of 64?
The integers that divide 64 without leaving any remainder are known as the factors of 64.
For example, 4 is a factor of 64 because when we divide 64 by 4, it leaves 16 as the quotient and 0 as the remainder. The quotient is also a factor of 64.
So, to check if the number is a factor of 64, divide 64 by that number and check if the remainder is zero or not.
Factor List of 64
The factors of 64 are 1, 2, 4, 8, 16, 32 and 64.
Prime Factorization of 64
The number 64 is a composite number, that is, it has more than two factors. To find the prime factorization of 64, we continue dividing 64 by its prime factors till we get 1 as the result.
First, we will divide 64 by its smallest prime factor, that is, 2.
64 ÷ 2 = 32
Continue dividing by 2:
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 64 = 2 × 2 × 2 × 2 × 2 × 2 or \(2^6 \)
This means that 2 is the only prime factor of 64.
The factor tree of 64 can be written as:
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Factor Pairs of 64
The factor pairs of 64 are two factors of 64 that, when multiplied together, give 64 as the result.
Example: (8, 8) is the factor pair of 64, as 8 \(\times \) 8 = 64
Positive Factor Pairs of 64
Hence, the positive factor pairs of 64 are (1, 64), (2, 32), (4, 16) and (8, 8).
Rapid Recall
The factors of 64 are:
Solved Examples
Example 1: Find the common factors of 64 and 56.
Solution:
The factors of 64 = 1, 2, 4, 8, 16, 32 and 64
The factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56
Therefore, the common factors of 64 and 56 are 1, 2, 4 and 8.
Example 2: Find the common factors of 64 and 120.
Solution:
The factors of 64 = 1, 2, 4, 8, 16, 32 and 64
The Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
Therefore, the common factors of 64 and 120 are 1, 2, 4 and 8.
Example 3: Find the common factors of 67 and 64.
Solution:
The factors of 67 = 1 and 67
The factors of 64 = 1, 2, 4, 8, 16, 32 and 64
Therefore, the common factor of 67 and 64 is 1.
The factors of 64 are 1, 2, 4, 8, 16, 32 and 64
So, the least factor of 64 is 1, and the greatest factor of 64 is 64 itself.
The factors of 64 are 1, 2, 4, 8, 16, 32 and 64.
Sum of factors = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127
So, the sum of the factors of 64 is 127.
Yes, 8 is a factor of 64 because when 8 divides 64, it leaves 0 as the remainder.
The prime factorization of 64 is 2 × 2 × 2 × 2 × 2 × 2 or \(2^6 \).
The positive factor pairs of 64 are (1, 64), (2, 32), (4, 16) and (8, 8).