Factors of 160 Using Prime Factorization
Factors of 160
What are the Factors of 160?
Integers that divide 160 without leaving any remainder are known as factors of 160.
For example: 5 is a factor of 160 because when we divide 160 by 5, we get the quotient as 32 and remainder as 0. Here the quotient is also a factor of 160.
So, to check if a number is a factor of 160, divide 160 by that number and check if the remainder is zero or not.
Deriving Factor List of 160
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
Prime Factorization of 160
The number 160 is a composite number, that is, it has more than two numbers as factors. To express 160 as the product of its factors is termed as the prime factorization of 160. To find the prime factors of 160, we will divide 160 by its prime factors till we get the result as 1.
So,
160 ÷ 2 = 80
80 ÷ 2 = 40
40 ÷ 2 = 20
20 ÷ 2 = 10
10 ÷ 2 = 5
Now, divide by the next prime number, 5
5 ÷ 5 = 1
So the factor tree of 160 can be written as:
So, the prime factorization of 160 = 2 × 2 × 2 × 2 × 2 × 5 or \(2^5\times5\).
This means that 2 and 5 are the prime factors of 160.
Factor Pairs of 160
The pair of factors or factor pairs of 160 are two factors that when multiplied together give a result of 160.
For example, (10, 16) is a factor pair of 160, as 10\(\times\)16 = 160
Hence, the positive pair factors of 160 are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) and (10, 16).
Read More:
Rapid Recall
Factors of 160 are:
Solved Factors of 160 Examples
Example 1: Find the common factors of 160 and 200.
Solution:
Factors of 160 = 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160
Factors of 200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200
Therefore, the common factors of 160 and 200 are 1, 2, 4, 5, 8, 10, 20 and 40.
Example 2: Find the common factors of 160 and 163.
Solution:
Factors of 160 = 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160
Factors of 163 = 1 and 163
Therefore, the common factor of 160 and 163 is 1.
Example 3: Courteney has 160 pens and she distributes them into red, green and yellow boxes. She distributes the pens such that she places one into the red box, then into the green box and finally into the yellow box – then she starts again with the red box. She follows the same pattern till she has distributed all the pens. What color box would she place the last pen into?
Solution:
There are 3 colored boxes
\(\frac{160}{3}\) = 53R1
3 is not a factor of 160. Therefore, when 160 is divided by 3, we get a quotient of 53 and a remainder of 1.
So the 52nd pen would go into the yellow box, and the 53rd pen which is the last one would go into the red box.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160
So, the least factor of 160 is 1 and the greatest factor of 160 is 160 itself.
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160
Sum of factors = 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 32 + 40 + 80 + 160 = 378
So, the sum of factors of 160 is 378.
Yes, 8 is a factor of 160. Because when 160 is divided by 8, we get the quotient as 20 and the remainder as 0.
The prime factorization of 160 is 2 × 2 × 2 × 2 × 2 × 5 or \(2^5\times5\).
The positive pair factors of 160 are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) and (10, 16).