# Factors of 70

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70

#### How to find factors of a number

 1.   Find factors of 70 using Division Method 2.   Find factors of 70 using Prime Factorization 3.   Find factors of 70 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 70

• Divide 70 by 1: 70 ÷ 1 : Remainder = 0
• Divide 70 by 2: 70 ÷ 2 : Remainder = 0
• Divide 70 by 5: 70 ÷ 5 : Remainder = 0
• Divide 70 by 7: 70 ÷ 7 : Remainder = 0
• Divide 70 by 10: 70 ÷ 10 : Remainder = 0
• Divide 70 by 14: 70 ÷ 14 : Remainder = 0
• Divide 70 by 35: 70 ÷ 35 : Remainder = 0
• Divide 70 by 70: 70 ÷ 70 : Remainder = 0

Hence, Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70

#### 2. Steps to find factors of 70 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 70 using the division method, follow these steps:

• Step 1. Start dividing 70 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 70, which is 2. Divide 70 by 2 to obtain the quotient (35).
70 ÷ 2 = 35
• Step 3. Repeat step 1 with the obtained quotient (35).
35 ÷ 5 = 7
7 ÷ 7 = 1

So, the prime factorization of 70 is, 70 = 2 x 5 x 7.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 70 as shown below:

So, the prime factorization of 70 is, 70 = 2 x 5 x 7.

#### 3. Find factors of 70 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 70 would be the two numbers which, when multiplied, give 70 as the result.

The following table represents the calculation of factors of 70 in pairs:

Factor Pair Pair Factorization
1 and 70 1 x 70 = 70
2 and 35 2 x 35 = 70
5 and 14 5 x 14 = 70
7 and 10 7 x 10 = 70

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 70. They are called negative pair factors.

Hence, the negative pairs of 70 would be ( -1 , -70 ) , ( -2 , -35 ) , ( -5 , -14 ) and ( -7 , -10 ) .

#### 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

• Each number is a factor of itself. Eg. 70 is a factor of itself.
• 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, 2, 5, 7, 10, 14, 35, 70 are exact divisors of 70.
• 1 is a factor of every number. Eg. 1 is a factor of 70.
• Every number is a factor of zero (0), since 70 x 0 = 0.

• Which is the smallest prime factor of 70?

The smallest prime factor of 70 is 2.

• Is 70 a whole number?

Yes 70 is a whole number.

• What are the prime factors of 70?

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
Prime factors of 70 are 2, 5, 7.

• What two numbers make 70?

Two numbers that make 70 are 2 and 35.

• What are multiples of 70?

First five multiples of 70 are 140, 210, 280, 350.

• What is the sum of all factors of 70?

The sum of all factors of 70 is 144.

• What are five multiples of 70?

First five multiples of 70 are 140, 210, 280, 350, 420.

• Is 70 a perfect square?

No 70 is not a perfect square.

• What is the greatest prime factors of 70?

The greatest prime factor of 70 is 7.

#### Examples of Factors

How many factors are there for 70?

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 70. Can you predict the answer?

7 factor(s) of 70 are 1, 2, 5, 7, 10, 14, 35.

Sammy is puzzled while calculating the prime factors of 70. Can you help him find them?

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
Prime factors of 70 are 2, 5, 7

What is prime factorization of 70?

Prime factorization of 70 is 2 x 5 x 7 = 2 x 5 x 7.

Ariel has been assigned the task to find the product of all the prime factors of 70. Can you help her?

Prime factors of 70 are 2, 5, 7.
Hence, the product of prime factors of 70.

Can you help Rubel to find out the product of the even factors of 70?

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
Even factors of 70 are 2, 10, 14, 70.
Hence, product of even factors of 70 is; 2 x 10 x 14 x 70 = 19600.

Joy wants to calculate mean of all the factors of 70. Help him in finding the mean of 70.

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 70 is 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 = 144.
Hence, the mean of factors of 70 is 144 ÷ 8 = 18.00.