Factors of 16 Using Prime Factorization
Factors of 16
What are the factors of 16?
Integers that divide 16 without leaving any remainder are known as factors of 16.
For example: 2 is a factor of 16 because when we divide 16 by 2 it gives us the quotient as 8 and the remainder as 0. Here the quotient is also a factor of 16.
So to check if the number is a factor of 16 or not, divide 16 by that number and check if the remainder is zero or not.
Factor list of 16
The factors of 16 are 1, 2, 4, 8, and 16.
Prime factors of 16
16 is a composite number, that is, it has more than two factors.
To find the prime factors of 16, we will divide 16 by its prime factors until we get the result as 1.
So, first let’s divide 16 by its smallest prime factor, that is, 2.
16 ÷ 2 = 8
Continue dividing by 2;
8 ÷ 4 = 2
4 ÷ 2 = 2
2 ÷ 2 = 1
So, the prime factorization of 16 = 2 × 2 × 2 × 2 or \(2^4\).
The factor tree of 16 can be written below as:
This means that 2 is the only prime factor of 16.
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Factor pairs of 16
A pair factor or a factor pair are two factors of 16 which when multiplied together give the result as 16.
Example: (2, 8) is a factor pair of 16.
Hence, the positive pair factors of 16 are (1, 16), (2, 8) and (4, 4).
Rapid Recall
Factors of 16 are;
Solved Example: Factors Of 16
Example 1: Find the common factors of 16 and 10.
Solution:
Factors of 16 = 1, 2, 4, 8 and 16
Factors of 10 = 1, 2, 5 and 10
Therefore, the common factors of 16 and 10 are 1 and 2.
Example 2: Find the common factors of 16 and 13.
Solution:
Factors of 16 = 1, 2, 4, 8 and 16
Factors of 13 = 1 and 13
Therefore, the common factor of 16 and 13 is 1.
Example 3: Find the common factors of 64 and 16.
Solution:
Factors of 64 = 1, 2, 4, 8, 16, 32 and 64
Factors of 16 = 1, 2, 4, 8 and 16
Therefore, the common factors of 64 and 16 are 1, 2, 4, 8 and 16.
The factors of 16 are 1, 2, 4, 8, and 16.
So, the least factor of 16 is 1 and the greatest factor is 16 itself.
The factors of 16 are 1, 2, 4, 8, and 16
Sum of factors = 1 + 2 + 4 + 8 + 16 = 31
So, the sum of factors of 16 is 31.
No, 14 is not a factor of 16. Because when 16 is divided by 14, it leaves the quotient as 1 and the remainder as 2. We know for a number to be a factor, on dividing we should get the remainder as 0. So, 14 is not a factor of 16.
The prime factorization of 16 is 2 × 2 × 2 × 2 or \(2^4\).
The positive pair factors of 16 are (1, 16), (2, 8) and (4, 4).