The factors of 46 are the numbers that completely divide 46 with the remainder zero. Thus we can say that the factors of 46 are the divisors of 46. In this section, we will learn about the factors of 46 and the prime factors of 46.

## Highlights of Factors of 46

- 46=2×23 is the prime factorization of 46.
- The factors of 46 are 1, 2, 23, and 46.
- Prime factors of 46 are 2 and 23.
- Negative factors of 46 are –1, -2, -23, and –46.

## What are the Factors of 46?

To find the factors of 46 by the multiplication method, let us write the number 46 multiplicatively in all possible ways. We have:

46 = 1×46 | ∴ 1, 46 are factors of 46 |

46 = 2×23 | ∴ 2, 23 are factors of 46 |

As we cannot express 46 multiplicatively in any other way, so we will stop right now. Note that the numbers in brown color are the factors of 46.

∴ the factors of 46 are 1, 2, 23, and 46.

We know that m is a factor of 46 if and only if -m is also a factor of 16. So the negative factors of 46 are -1, -2, -23, and -46.

## Pair Factors of 46

46 = a×b | Pair Factors of 46 |

46 = 1×46 | (1, 46) |

46 = 2×23 | (2, 23) |

Thus the positive pair factors of 46 are (1, 46) and (2, 23).

We know that if (a, b) is a positive pair factor of 46, then (-a, -b) is a negative pair factor of 46. As a result, we have obtained all the negative pair factors of 16, and they are (-1, -46) and (-2, -23).

## Number of Factors of 46

From above we have calculated the factors of 46 which are 1, 2, 23, and 46. Thus the total number of factors of 46 is four.

## Prime Factors of 46

Note that the factors of 46 are 1, 2, 23, and 46. Among those factors, we observe that only 2 and 23 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 46 are 2 and 23.

Question: What are the factors of 46?

Video Solution: coming soon…

**Also Read:**

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

Factors of 66: | 1, 2, 3, 6, 11, 22, 33, 66 |

Factors of 34: | 1, 2, 17, 34 |

Factors of 75: | 1, 3, 5, 15, 25, 75 |

## How to Find Factors of 46?

Now we will determine the factors of 46 by **division method**. In this method, we will find the numbers that can divide 46 with no remainder. See that

46/1=46 and the remainder is 0 | ∴ 1 and 46 are factors of 46 |

46/2=23 and the remainder is 0 | ∴ 2 and 23 are factors of 46 |

Note that no numbers other than the numbers in violet color can divide 46. So the numbers in violet color, that is, 1, 2, 23, and 46 are the complete list of factors of 46.