Factors of 16 are the set of integers that can divide 16 perfectly i.e when you divide it with its factors, we will get 0 as the remainder.
Let us see the factors in different ways to represent the factors, and various methods to find these factors.
- Factors: 1, 2, 4, 8 and 16
- Negative Factors: -1, -2, -4, -8 and -16
- Prime Factors: 2
- Prime Factorization: 2 × 2 × 2 × 2 = 24
- Sum of Factors: 31
- Factor pairs are (1, 16), (2, 8), and (4, 4)
Now the most used method to find factors in the prime factorization
Prime Factorization of 16
The prime factorization of a number refers to the process of writing the number as the product of its prime factors.
There are two methods of prime factorization which we can follow to find all the factors of a number
Prime Factorization Of 16 By Upside Down Division Method
The Prime Factorization by Upside Down Division Method is shown below:
Here, 16 is an even number. So it is undoubtedly divisible by 2 with no remainder.
Thus we do 16÷ 2 = 8.
Now find the prime factors of the obtained quotient.
Repeat Step 1 and Step 2 until we get a result of prime number as the quotient.
Here, 8 is the quotient.
8÷ 2 = 4. Here, 4 is the quotient.
Now find the prime factors of the 4.
4÷ 2= 2. Here, 2 is the quotient
2÷ 2= 1.
As the quotient is 1, we stop the process and all the left side numbers become the prime factors.
From this, we can get the prime of factorisation of 16 as 2*2*2*2 and a prime factor as 2.
Prime Factorization By Factor Tree Method
For this method, you must first consider two factors say a, b of the number such that a*b is equal to that number and then consider two factors of a and b each and so on. This process is repeated until the factors are prime.
You may have different factor trees depending on the starting point, however, all of them would show the same prime factors.
Factor Tree Method is shown below:
2 is a prime number. Hence, the factor tree ends there. Hence, prime factorization is 2 × 2 × 2 × 2 and the prime factor of 16 is 2.
The factors are 1, 2, 4, 8, 16.
Sum of all factors is 1 + 2 + 4 + 8 + 16 = 31