The factors of 32 are the numbers that completely divide 32 without leaving a remainder. Thus we can say that the factors of 32 are the divisors of 32. In this section, we will learn about the factors of 32 and the prime factors of 32.

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## Highlights of Factors of 32

**32=2×2×2×2×2=2**is the prime factorization of 32.^{5}- The factors of 32 are 1, 2, 4, 8, 16, and 32.
- 2 is the only prime factor of 32.
- The negative factors of 32 are –1, -2, -4, -8, -16, and –32.

## What are the Factors of 32?

To find the factors of 32, we need to write the number 32 multiplicatively in all possible ways. Note that we can write 32 as follows:

32 = 1×32

32 = 2×16

32 = 4×8

As there are no other ways we can express 32 multiplicatively, we will stop now. Hence the factors of 32 in pairs are given as follows:

32 = a×b | Factors in Pairs (a,b) |

32 = 1×32 | (1, 32) |

32 = 2×16 | (2, 16) |

32 = 4×8 | (4, 8) |

Thus the pair factors of 32 are (1, 32), (2, 16), and (4, 8). Since all the numbers appearing in pair factors are the factors of 32, we conclude that

The factors of 32 are: 1, 2, 4, 8, 16 and 32. |

## Number of factors of 32

From above we see that the factors of 32 are 1, 2, 4, 8, 16, and 32.

Thus the total number of factors of 32 is six.

## Prime Factors of 32

We have found above that the factors of 32 are 1, 2, 4, 8, 16, and 32. Among those factors, we observe that only 2 is a prime number as it does not have any proper divisors.

∴ the only prime factor of 32 is 2.

**Question:** What are the factors of 32?

**Video Solution:**

## How to Find Factors of 32?

By **division method**, we will determine the factors of 32. In this method, we will find the numbers that can divide 32 completely with the remainder zero. See that

32/1=32 and the remainder is 0.

∴ 1 and 32 are factors of 32.

32/2=16 and the remainder is 0.

∴ 2 and 16 are factors of 32.

32/4=8 and the remainder is 0.

∴ 4 and 8 are factors of 32.

Note that no numbers other than the numbers in violet color can divide 32. So the numbers in violet color, that is, 1, 2, 4, 8, 16, and 32 are the complete list of factors of 32.