A factor of 35 is a number that completely divides 35 with the remainder zero. Thus the factors of 35 are the divisors of 35. In this section, we will learn about the factors of 35 and the prime factors of 35.

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## Highlights of Factors of 35

**35=5×7.**This is the prime factorization of 35.- The factors of 35 are 1, 5, 7, and 35.
- Prime factors of 35 are 5 and 7.
- Negative factors of 35 are –1, -5, -7, and –35.

## What are the Factors of 35?

Let us write the number 35 multiplicatively in all possible ways.

35 = 1×35

35 = 5×7

As we can write 35 multiplicatively in no other ways, so we will stop right now. So the factors of 35 in pairs are given as follows:

35 = a×b | Factors in Pairs (a,b) |

35 = 1×35 | (1, 35) |

35 = 5×7 | (5, 7) |

Thus the pair factors of 35 are (1, 35) and (5, 7). Since all the numbers appearing in pair factors are the factors of 35, we conclude that

The factors of 35 are: 1, 5, 7, and 35. |

## Number of Factors of 35

As the factors of 35 are 1, 5, 7, and 35, we see that the total number of factors of 35 is four.

## Prime Factors of 35

Note that the factors of 35 are 1, 5, 7, and 35. Among those factors, we observe that only 5 and 7 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 35 are 5 and 7.

Question: What are the factors of 35?

Video Solution:

## How to Find Factors of 35?

Now we will determine the factors of 35 by **division method**. In this method, we will try to find the numbers that can divide 35 with no remainder. See that

35/1=35 and the remainder is 0.

∴ 1 and 35 are factors of 35.

35/5=7 and the remainder is 0.

∴ 5 and 7 are factors of 35.

Note that no numbers other than the numbers in violet color can divide 35. So the numbers in violet color, that is, 1, 5, 7 and 35 are the complete list of factors of 35.