What are the factors of 40? The factors of 40 are the numbers that completely divide 40 without leaving a remainder. Thus we can say that the factors of 40 are the divisors of 40. In this section, we will learn about the factors of 40 and the prime factors of 40.

## Highlights of Factors of 40

- 40=2×2×2×5 is the prime factorization of 40.
- The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
- 2 and 5 are the prime factors of 40.
- The negative factors of 40 are –1, -2, -4, -5, -8, -10, -20, and –40.

## What are the Factors of 40?

To get the factors of 40, we will first write the number 40 multiplicatively in all possible ways. We can write 40 as follows and get all the factors of 40.

40 = 1×40 | ∴ 1, 40 are factors of 40 |

40 = 2×20 | ∴ 2, 20 are factors of 40 |

40 = 4×10 | ∴ 4, 10 are factors of 40 |

40 = 5×8 | ∴ 5, 8 are factors of 40 |

Note that we cannot express 40 multiplicatively in any way other than the above ones, so we will stop now. Hence the factors of 40 are the numbers in brown color.

∴ we conclude that the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

We know that m is a factor of 40 if and only if -m is a factor of 40. Thus all the negative factors of 40 are -1, -2, -4, -5, -8, -10, -20, and -40.

## Pair Factors of 40

40 = a×b | Factors in Pairs (a,b) |

40 = 1×40 | (1, 40) |

40 = 2×20 | (2, 20) |

40 = 4×10 | (4, 10) |

40 = 5×8 | (5, 8) |

Thus the pair factors of 40 are (1, 40), (2, 20), (4, 10), and (5, 8).

If (a, b) is a pair factor of 40 if and only if (-a, -b) is a negative pair factor of 40. So all the negative pair factors of 40 are (-1, -40), (-2, -20), (-4, -10), and (-5, -8).

## Number of Factors of 40

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Therefore the total number of factors of 40 is eight.

## Prime Factors of 40

We have found above that the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Among those factors, we observe that only 2 and 5 is the prime number as it does not have any proper divisors.

∴ the prime factors of 40 are 2 and 5.

**Question:** What are the factors of 40?

**Video Solution:**

**Also Read:**

Factors of 32: | 1, 2, 4, 8, 16, 32 |

Factors of 25: | 1, 5, 25 |

Factors of 35: | 1, 5, 7, 35 |

Factors of 44: | 1, 2, 4, 11, 22, 44 |

## How to Find Factors of 40?

By **division method**, we will determine the factors of 40. In this method, we will find the numbers that can divide 40 completely with the remainder zero. See that

40/1=40 and the remainder is 0 | ∴ 1 and 40 are factors of 40 |

40/2=20 and the remainder is 0 | ∴ 2 and 20 are factors of 40 |

40/4=10 and the remainder is 0 | ∴ 4 and 10 are factors of 40 |

40/5=8 and the remainder is 0 | ∴ 5 and 8 are factors of 40 |

Note that no numbers other than the numbers in violet color can divide 40. So the numbers in violet color, that is, 1, 2, 4, 5, 8, 10, 20, and 40 are the complete list of factors of 40.