# Factors of 136

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, and 136

#### How to find factors of a number

 1.   Find factors of 136 using Division Method 2.   Find factors of 136 using Prime Factorization 3.   Find factors of 136 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 136

• Divide 136 by 1: 136 ÷ 1 : Remainder = 0
• Divide 136 by 2: 136 ÷ 2 : Remainder = 0
• Divide 136 by 4: 136 ÷ 4 : Remainder = 0
• Divide 136 by 8: 136 ÷ 8 : Remainder = 0
• Divide 136 by 17: 136 ÷ 17 : Remainder = 0
• Divide 136 by 34: 136 ÷ 34 : Remainder = 0
• Divide 136 by 68: 136 ÷ 68 : Remainder = 0
• Divide 136 by 136: 136 ÷ 136 : Remainder = 0

Hence, Factors of 136 are 1, 2, 4, 8, 17, 34, 68, and 136

#### 2. Steps to find factors of 136 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 136 using the division method, follow these steps:

• Step 1. Start dividing 136 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 136, which is 2. Divide 136 by 2 to obtain the quotient (68).
136 ÷ 2 = 68
• Step 3. Repeat step 1 with the obtained quotient (68).
68 ÷ 2 = 34
34 ÷ 2 = 17
17 ÷ 17 = 1

So, the prime factorization of 136 is, 136 = 2 x 2 x 2 x 17.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 136 as shown below:

So, the prime factorization of 136 is, 136 = 2 x 2 x 2 x 17.

#### 3. Find factors of 136 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 136 would be the two numbers which, when multiplied, give 136 as the result.

The following table represents the calculation of factors of 136 in pairs:

Factor Pair Pair Factorization
1 and 136 1 x 136 = 136
2 and 68 2 x 68 = 136
4 and 34 4 x 34 = 136
8 and 17 8 x 17 = 136

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 136. They are called negative pair factors.

Hence, the negative pairs of 136 would be ( -1 , -136 ) , ( -2 , -68 ) , ( -4 , -34 ) and ( -8 , -17 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 136 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 136.
• Every number is a factor of zero (0), since 136 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, 2, 4, 8, 17, 34, 68, 136 are exact divisors of 136.
• Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136. Each factor divides 136 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 8, 17, 34, 68, 136 are all less than or equal to 136.

• What are the prime factors of 136?

The factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.
Prime factors of 136 are 2, 2, 2, 17.

• What is the sum of all factors of 136?

The sum of all factors of 136 is 270.

• What are the pair factors of 136?

Pair factors of 136 are (1,136), (2,68), (4,34), (8,17).

• What two numbers make 136?

Two numbers that make 136 are 2 and 68.

• What are multiples of 136?

First five multiples of 136 are 272, 408, 544, 680.

• Is 136 a perfect square?

No 136 is not a perfect square.

• Which is greatest factor of 136?

The greatest factor of 136 is 68.

• How do you factors of 136?

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.

• What are five multiples of 136?

First five multiples of 136 are 272, 408, 544, 680, 816.

#### Examples of Factors

Can you help Rubel to find out the product of the even factors of 136?

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.
Even factors of 136 are 2, 4, 8, 34, 68, 136.
Hence, product of even factors of 136 is; 2 x 4 x 8 x 34 x 68 x 136 = 20123648.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 136? Help her in writing all the factors.

Positive factors are 1, 2, 4, 8, 17, 34, 68, 136.
Negative factors are -1, -2, -4, -8, -17, -34, -68, -136.

How many factors are there for 136?

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.
So there are in total 8 factors.

Sammy is puzzled while calculating the prime factors of 136. Can you help him find them?

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.
Prime factors of 136 are 2, 2, 2, 17

Joey wants to write all the prime factors of 136 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 136 are 2, 2, 2, 17.
So in exponential form it can be written as 23 x 17.

What is prime factorization of 136?

Prime factorization of 136 is 2 x 2 x 2 x 17 = 23 x 17.

Can you help Rubel to find out the product of the even factors of 136?

Factors of 136 are 1, 2, 4, 8, 17, 34, 68, 136.
Even factors of 136 are 2, 4, 8, 34, 68, 136.
Hence, product of even factors of 136 is; 2 x 4 x 8 x 34 x 68 x 136 = 20123648.