The factors of 160 are the numbers that divide the number 160 completely without leaving any remainder values. The factors of 160 can be represented in both positive and negative form. For example, the pair factor of 160 is expressed as (1, 160) or (-1, -160). The multiplication of -1 and -160 gives the product value 160. But, the factors of 160 cannot be in decimal or fractional form.
In this article, we will learn the factors of 160, positive and negative pair factors of 160, prime factors of 160 using the prime factorization method and many solved examples.
Table of Contents:
- What are the Factors of 160?
- Pair Factors of 160
- Factors of 160 by Division Method
- Prime Factorization of 160
- Solved Examples
- FAQs
What are the Factors of 160?
The numbers that divide 160 evenly and leave a remainder value of 0 are the factors of 160. As the number 160 is an even composite number, it has more than two factors. The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160. Similarly, the negative factors of 160 are -1, -2, -4, -5, -8, -10, -16, -20, -32, -40, -80 and -160.
Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160. Prime Factorization of 160: 2 × 2 × 2 × 2 × 2 × 5 or 2^{5 }× 5. |
Pair Factors of 160
As discussed above, the pair factors of 160 can be expressed in both positive and negative form. A pair of numbers multiplied together, resulting in the original number 160, is called the pair factor of 160. The following are the positive and negative pair factors of 160.
Positive Pair Factors of 160:
Positive Factors of 160 |
Positive Pair Factors of 160 |
1 × 160 |
(1, 160) |
2 × 80 |
(2, 80) |
4 × 40 |
(4, 40) |
5 × 32 |
(5, 32) |
8 × 20 |
(8, 20) |
10 × 16 |
(10, 16) |
Therefore, the positive pair factors of 160 are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) and (10, 16).
Negative Pair Factors of 160:
Negative Factors of 160 |
Negative Pair Factors of 160 |
-1 × -160 |
(-1, -160) |
-2 × -80 |
(-2, -80) |
-4 × -40 |
(-4, -40) |
-5 × -32 |
(-5, -32) |
-8 × -20 |
(-8, -20) |
-10 × -16 |
(-10, -16) |
Therefore, the negative pair factors of 160 are (-1, -160), (-2, -80), (-4, -40), (-5, -32), (-8, -20) and (-10, -16).
Note: If (m, n) is a pair factor of a number, we can also consider (n, m) as a pair factor of a number.
Factors of 160 by Division Method
In the division method, the factors of 160 are found by dividing the number 160 by different integer numbers. If the integer divides 160 evenly without leaving a remainder, then the integer is a factor of 160. Now, let us start dividing 160 by 1 and then continue with the different integers.
- 160/1 = 160 (Factor is 1 and Remainder is 0)
- 160/2 = 80 (Factor is 2 and Remainder is 0)
- 160/4 = 40 (Factor is 4 and Remainder is 0)
- 160/5 = 32 (Factor is 5 and Remainder is 0)
- 160/8 = 20 (Factor is 8 and Remainder is 0)
- 160/10 = 16 (Factor is 10 and Remainder is 0)
- 160/16 = 10 (Factor is 16 and Remainder is 0)
- 160/20 = 8 (Factor is 20 and Remainder is 0)
- 160/32 = 5 (Factor is 32 and Remainder is 0)
- 160/40 = 4 (Factor is 40 and Remainder is 0)
- 160/80 = 2 (Factor is 80 and Remainder is 0)
- 160/160 = 1 (Factor is 160 and Remainder is 0)
If we divide 160 by any numbers other than 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160, it leaves a remainder of some integer value. Therefore, the factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
Prime Factorization of 160
The method of writing the number 160 as the product of its prime factors is called the prime factorization of 160. Go through the following procedure to find the prime factors of 160.
Take a pair factor of 160, say (1, 160)
Here, 160 is an even composite number, which can be further split as the product of 10 and 16.
Now, both the numbers 10 and 16 are composite and can be split further into their prime factors.
Thus, the number 10 and 16 are written as follows:
10 = 2 × 5
16 = 2 × 2 × 2 × 2
Therefore, the prime factorization of 160 is 2 × 2 × 2 × 2 × 2 × 5 or 2^{5 }× 5, where 2 and 5 are prime numbers.
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Solved Examples
Example 1:
Find the common factors of 160 and 159.
Solution:
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
The factors of 159 are 1, 3, 53 and 159.
Thus, the common factor of 160 and 159 is 1.
Example 2:
What are the common factors of 160 and 161?
Solution:
Factors of 160 = 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
Factors of 161 = 1, 7, 23 and 161.
Hence, the common factor of 160 and 161 is 1.
Example 3:
Find the common factors of 160 and 80.
Solution:
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
Therefore, the common factors of 160 and 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80.
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Frequently Asked Questions on Factors of 160
What are the factors of 160?
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80 and 160.
What is the prime factorization of 160?
The prime factorization of 160 is 2 × 2 × 2 × 2 × 2 × 5 or 2^{5} × 5.
What are the positive pair factors of 160?
The positive pair factors of 160 are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) and (10, 16).
What are the negative pair factors of 160?
The negative pair factors of 160 are (-1, -160), (-2, -80), (-4, -40), (-5, -32), (-8, -20) and (-10, -16).
Is 32 a factor of 160?
Yes, 32 is a factor of 160. If 160 is divisible by 32, it leaves a quotient value of 5 and remainder 0, and hence, 32 is a factor of 160.