# Factors of 35

Factors of 35 are 1, 5, 7, and 35

#### How to find factors of a number

 1.   Find factors of 35 using Division Method 2.   Find factors of 35 using Prime Factorization 3.   Find factors of 35 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 35

• Divide 35 by 1: 35 ÷ 1 : Remainder = 0
• Divide 35 by 5: 35 ÷ 5 : Remainder = 0
• Divide 35 by 7: 35 ÷ 7 : Remainder = 0
• Divide 35 by 35: 35 ÷ 35 : Remainder = 0

Hence, Factors of 35 are 1, 5, 7, and 35

#### 2. Steps to find factors of 35 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 35 using the division method, follow these steps:

• Step 1. Start dividing 35 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 35, which is 5. Divide 35 by 5 to obtain the quotient (7).
35 ÷ 5 = 7
• Step 3. Repeat step 1 with the obtained quotient (7).
7 ÷ 7 = 1

So, the prime factorization of 35 is, 35 = 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 35 as shown below:

So, the prime factorization of 35 is, 35 = 5 x 7.

#### 3. Find factors of 35 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 35 would be the two numbers which, when multiplied, give 35 as the result.

The following table represents the calculation of factors of 35 in pairs:

Factor Pair Pair Factorization
1 and 35 1 x 35 = 35
5 and 7 5 x 7 = 35

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 35. They are called negative pair factors.

Hence, the negative pairs of 35 would be ( -1 , -35 ) , ( -5 , -7 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 35 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 5, 7, 35 are exact divisors of 35.
• Factors of 35 are 1, 5, 7, 35. Each factor divides 35 without leaving a remainder.

• What is prime factorization of 35?

Prime factorization of 35 is 5 x 7.

• How do you find factors of a negative number? ( eg. -35 )?

Factors of -35 are -1, -5, -7, -35.

• What are the prime factors of 35?

The factors of 35 are 1, 5, 7, 35.
Prime factors of 35 are 5, 7.

• What are pair factors of 35?

The pair factors of 35 are (1,35), (5,7).

• What is the greatest prime factors of 35?

The greatest prime factor of 35 is 7.

• What are six multiples of 35?

First five multiples of 35 are 70, 105, 140, 175, 210, 245.

• What are factors of 35?

Factors of 35 are 1, 5, 7, 35.

• Which is the smallest prime factor of 35?

Smallest prime factor of 35 is 5.

• Is 35 a whole number?

Yes 35 is a whole number.

#### Examples of Factors

Kevin has been asked to write 3 factor(s) of 35. Can you predict the answer?

3 factor(s) of 35 are 1, 5, 7.

Sammy is puzzled while calculating the prime factors of 35. Can you help him find them?

Factors of 35 are 1, 5, 7, 35.
Prime factors of 35 are 5, 7

What is prime factorization of 35?

Prime factorization of 35 is 5 x 7 = 5 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 35. Can you help her?

Prime factors of 35 are 5, 7.
Hence, the product of prime factors of 35.

Can you help Rubel to find out the product of the even factors of 35?

Factors of 35 are 1, 5, 7, 35.
Even factors of 35 are 0.
Hence, product of even factors of 35 is; 0 = 0.

Joy wants to calculate mean of all the factors of 35. Help him in finding the mean of 35.

Factors of 35 are 1, 5, 7, 35.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 35 is 1 + 5 + 7 + 35 = 48.
Hence, the mean of factors of 35 is 48 ÷ 4 = 12.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 35? Help her in writing all the factors.

Positive factors are 1, 5, 7, 35.
Negative factors are -1, -5, -7, -35.