The factors of 56 are the numbers that completely divide 56 without leaving a remainder. Thus, we can say that the factors of 56 are the divisors of 56. In this section, we will learn about the factors of 56 and the prime factors of 56. Note that we have:

- 56 = 2×2×2×7= 2
^{3}×7 is the prime factorization of 56. - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
- The prime factors of 56 are 2 and 7.
- Negative factors of 56 are –1, -2, -4,-7, -8, -14, -28, and –56.

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## What are the Factors of 56?

Let us write the number 56 multiplicatively in all possible ways. We definitely have:

56 = 1×56

56 = 2×28

56 = 4×14

56 = 7×8

As there are no numbers between 7 and 8 that can divide 56, so we will stop writing 56 multiplicatively right now. So the factors of 56 in pairs are given as follows:

56 = a×b | Factors in Pairs (a,b) |

56 = 1×56 | (1, 56) |

56 = 2×28 | (2, 28) |

56 = 4×14 | (4, 14) |

56 = 7×8 | (7, 8) |

Thus the pair factors of 56 are (1, 56), (2, 28), (4, 14), and (7, 8). As all the numbers appearing in pair factors are the factors of 56, we conclude that

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56. |

## Number of Factors of 56

From above we have calculated the factors of 56 which are 1, 2, 4, 7, 8, 14, 28, and 56.

Thus the total number of factors of 56 is eight.

## Prime Factors of 56

Note that the factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. Among those factors, we observe that only 2 and 7 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 56 are 2 and 7.

Question: What are the factors of 56?

Video Solution:

## How to Find Factors of 56?

Now we will determine the factors of 56 by **division method**. In this method, we will try to find the numbers that can divide 56 with no remainder. See that

56/1=56 and the remainder is 0 | ∴ 1 and 56 are factors of 56 |

56/2=28 and the remainder is 0 | ∴ 2 and 28 are factors of 56. |

56/4=14 and the remainder is 0 | ∴ 4 and 14 are factors of 56. |

56/7=8 and the remainder is 0 | ∴ 7 and 8 are factors of 56. |

Note that no numbers other than the numbers in violet color can divide 56. So the numbers in violet color, that is, 1, 2, 4, 7, 8, 14, 28, and 56 are the complete list of factors of 56.

**Also Read: **

- Basic concepts of factors
- Square root of 56
- Cube root of 56
- Divisors of 56

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.