# Factors of 156

Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156

#### How to find factors of a number

 1.   Find factors of 156 using Division Method 2.   Find factors of 156 using Prime Factorization 3.   Find factors of 156 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 156

• Divide 156 by 1: 156 ÷ 1 : Remainder = 0
• Divide 156 by 2: 156 ÷ 2 : Remainder = 0
• Divide 156 by 3: 156 ÷ 3 : Remainder = 0
• Divide 156 by 4: 156 ÷ 4 : Remainder = 0
• Divide 156 by 6: 156 ÷ 6 : Remainder = 0
• Divide 156 by 12: 156 ÷ 12 : Remainder = 0
• Divide 156 by 13: 156 ÷ 13 : Remainder = 0
• Divide 156 by 26: 156 ÷ 26 : Remainder = 0
• Divide 156 by 39: 156 ÷ 39 : Remainder = 0
• Divide 156 by 52: 156 ÷ 52 : Remainder = 0
• Divide 156 by 78: 156 ÷ 78 : Remainder = 0
• Divide 156 by 156: 156 ÷ 156 : Remainder = 0

Hence, Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156

#### 2. Steps to find factors of 156 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 156 using the division method, follow these steps:

• Step 1. Start dividing 156 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 156, which is 2. Divide 156 by 2 to obtain the quotient (78).
156 ÷ 2 = 78
• Step 3. Repeat step 1 with the obtained quotient (78).
78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1

So, the prime factorization of 156 is, 156 = 2 x 2 x 3 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 156 as shown below:

So, the prime factorization of 156 is, 156 = 2 x 2 x 3 x 13.

#### 3. Find factors of 156 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 156 would be the two numbers which, when multiplied, give 156 as the result.

The following table represents the calculation of factors of 156 in pairs:

Factor Pair Pair Factorization
1 and 156 1 x 156 = 156
2 and 78 2 x 78 = 156
3 and 52 3 x 52 = 156
4 and 39 4 x 39 = 156
6 and 26 6 x 26 = 156
12 and 13 12 x 13 = 156

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 156. They are called negative pair factors.

Hence, the negative pairs of 156 would be ( -1 , -156 ) , ( -2 , -78 ) , ( -3 , -52 ) , ( -4 , -39 ) , ( -6 , -26 ) and ( -12 , -13 ) .

#### 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. 156 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 156.
• Every number is a factor of zero (0), since 156 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, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 are exact divisors of 156.
• Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156. Each factor divides 156 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156 are all less than or equal to 156.

• What are the prime factors of 156?

The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Prime factors of 156 are 2, 2, 3, 13.

• What two numbers make 156?

Two numbers that make 156 are 2 and 78.

• What is the greatest prime factors of 156?

The greatest prime factor of 156 is 13.

• What are factors of 156?

Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.

• How do you find factors of a negative number? ( eg. -156 )?

Factors of -156 are -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, -156.

• What are five multiples of 156?

First five multiples of 156 are 312, 468, 624, 780, 936.

• Write some multiples of 156?

First five multiples of 156 are 312, 468, 624, 780.

• Is 156 a perfect square?

No 156 is not a perfect square.

• What two numbers make 156?

Two numbers that make 156 are 2 and 78.

#### Examples of Factors

What is prime factorization of 156?

Prime factorization of 156 is 2 x 2 x 3 x 13 = 22 x 3 x 13.

Sammy is puzzled while calculating the prime factors of 156. Can you help him find them?

Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Prime factors of 156 are 2, 2, 3, 13

Kevin has been asked to write 11 factor(s) of 156. Can you predict the answer?

11 factor(s) of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78.

Joey wants to write all the prime factors of 156 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 156 are 2, 2, 3, 13.
So in exponential form it can be written as 22 x 3 x 13.

How many factors are there for 156?

Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
So there are in total 12 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 156? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Negative factors are -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, -156.

Can you help Rubel to find out the product of the even factors of 156?

Factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156.
Even factors of 156 are 2, 4, 6, 12, 26, 52, 78, 156.
Hence, product of even factors of 156 is; 2 x 4 x 6 x 12 x 26 x 52 x 78 x 156 = 9475854336.