The factors of 56 are the numbers, which produce the result as 56 when two numbers are multiplied together. Factor pairs of the number 56 are the whole numbers which could be either positive or negative but not a fraction or decimal number. Consider an example, the factor pair of 56 is written as (1, 56) and (-1, -56). Thus, we can consider both positive and negative factor pairs of 11. To find the factors of a number, 56, we will use the factorization method. In this article, we will learn the factors of 56, pair factors and the prime factors of 56 using the prime factorization method with many solved examples.
Table of Contents:
- What are the Factors of 56?
- Pair Factors of 56
- Factors of 56 by Division Method
- Prime Factorization of 56
- Solved Examples
- FAQs
What are the Factors of 56?
The numbers that divide 56 exactly are the factors of 56. In other words, the numbers which are multiplied in pairs resulting in 56 are the factors of 56. As the number 56 is an even composite number, it has many factors other than 1 and 56. Thus, the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56. Prime Factorization of 56: 2×2×2×7 or 2^{3 }× 7. |
Pair Factors of 56
To find the pair factors, multiply the two numbers in a pair to get the original number as 56, such numbers are as follows
Positive pair Factors | Negative Pair Factors |
1 × 56 = 56 ⇒(1, 56) | -1 × -56 = 56 ⇒(-1, -56) |
2 × 28 = 56 ⇒ (2, 28) | -2 × -28 = 56 ⇒ (-2, -28) |
4 × 14 = 56 ⇒ (4, 14) | -4 × -14 = 56 ⇒ (-4, -14) |
7 × 8 = 56 ⇒(7, 8) | -7 × -8 = 56 ⇒(-7, -8) |
Therefore, the positive pair factors of 56 are (1, 56), (2, 28), (4, 14) and (7, 8). Similarly, the negative pair factors of 56 are (-1, -56), (-2, -28), (-4, -14) and (-7, -8).
Factors of 56 by Division Method
In the division method, the factors of 56 can be found by dividing 56 by different consecutive integers. If the integers divide 56 exactly, then those integers are the factors of 56. Now, let us start dividing 56 by 1 and then continue with the different integer numbers.
- 56/1 = 56 (Factor = 1 and remainder = 0)
- 56/2 = 28 (Factor = 2 and remainder = 0)
- 56/4 = 14 (Factor = 4 and remainder = 0)
- 56/7 = 8 (Factor = 7 and remainder = 0)
- 56/8 = 7 (Factor = 8 and remainder = 0)
- 56/14 = 4 (Factor = 14 and remainder = 0)
- 56/28 = 2 (Factor = 28 and remainder = 0)
- 56/56 = 1 (Factor = 56 and remainder =0)
Thus, the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
Note:
If we divide 56 by numbers other than 1, 2, 4, 7, 8, 14, 28 and 56, it leaves a remainder and hence, they are not the factors of 56.
Prime Factorization of 56
The number 56 is a composite number and it has prime factors. Now let us know how to find the prime factors of a number.
- The first step is to divide the number 56 with the smallest prime factor, say 2.
56 ÷ 2 = 28
- Again, divide 28 by 2 and the process goes on.
28 ÷ 2 = 14
14 ÷ 2 = 7
- Now, if we divide 7 by 2 we will get a fractional number, which cannot be a factor. So, now proceed with the next prime numbers, i.e. 7
- 7 ÷ 7 = 1
- We have received 1 at the end of the division process and so that we cannot proceed further. So, the prime factors are written as 2 × 2 × 2 × 7 or 2^{3} × 7, where 2 and 7 are the prime numbers.
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Examples
Example 1:
Find the common factors of 56 and 57.
Solution:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56
The factors of 57 are 1, 3, 19 and 57.
Thus, the common factor of 56 and 57 is 1.
Example 2:
Find the common factors of 56 and 55.
Solution:
Factors of 56 = 1, 2, 4, 7, 8, 14, 28 and 56
The factors of 55 = 1, 5, 11 and 55.
Thus, the common factor of 56 and 55 is 1.
Example 3:
Find the common factors of 56 and 65.
Solution:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
The factors of 65 are 1, 5, 13 and 65.
Hence, the common factor of 56 and 65 is 1 only.
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Frequently Asked Questions on Factors of 56
What are the Factors of 56?
The factors of 56 are the numbers that are multiplied in pairs resulting in an original number 56. Thus, the factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56.
What is the prime factorization of 56?
The prime factorization of 56 is 2×2×2×7 or 2^{3} × 7
What are the positive pair factors of 56?
The positive pair factors of 56 are (1, 56), (2, 28), (4, 14) and (7, 8).
What are the negative pair factors of 56?
The negative pair factors of 56 are (-1, -56), (-2, -28), (-4, -14) and (-7, -8).
Is 14 a factor of 56?
Yes, 14 is a factor of 56. If 56 is divided by 14, it leaves the remainder 0, and hence, 14 is a factor of 56.