# Factors of 312

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312

#### How to find factors of a number

 1.   Find factors of 312 using Division Method 2.   Find factors of 312 using Prime Factorization 3.   Find factors of 312 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 312

• Divide 312 by 1: 312 ÷ 1 : Remainder = 0
• Divide 312 by 2: 312 ÷ 2 : Remainder = 0
• Divide 312 by 3: 312 ÷ 3 : Remainder = 0
• Divide 312 by 4: 312 ÷ 4 : Remainder = 0
• Divide 312 by 6: 312 ÷ 6 : Remainder = 0
• Divide 312 by 8: 312 ÷ 8 : Remainder = 0
• Divide 312 by 12: 312 ÷ 12 : Remainder = 0
• Divide 312 by 13: 312 ÷ 13 : Remainder = 0
• Divide 312 by 24: 312 ÷ 24 : Remainder = 0
• Divide 312 by 26: 312 ÷ 26 : Remainder = 0
• Divide 312 by 39: 312 ÷ 39 : Remainder = 0
• Divide 312 by 52: 312 ÷ 52 : Remainder = 0
• Divide 312 by 78: 312 ÷ 78 : Remainder = 0
• Divide 312 by 104: 312 ÷ 104 : Remainder = 0
• Divide 312 by 156: 312 ÷ 156 : Remainder = 0
• Divide 312 by 312: 312 ÷ 312 : Remainder = 0

Hence, Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312

#### 2. Steps to find factors of 312 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 312 using the division method, follow these steps:

• Step 1. Start dividing 312 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 312, which is 2. Divide 312 by 2 to obtain the quotient (156).
312 ÷ 2 = 156
• Step 3. Repeat step 1 with the obtained quotient (156).
156 ÷ 2 = 78
78 ÷ 2 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1

So, the prime factorization of 312 is, 312 = 2 x 2 x 2 x 3 x 13.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 312 as shown below:

So, the prime factorization of 312 is, 312 = 2 x 2 x 2 x 3 x 13.

#### 3. Find factors of 312 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 312 would be the two numbers which, when multiplied, give 312 as the result.

The following table represents the calculation of factors of 312 in pairs:

Factor Pair Pair Factorization
1 and 312 1 x 312 = 312
2 and 156 2 x 156 = 312
3 and 104 3 x 104 = 312
4 and 78 4 x 78 = 312
6 and 52 6 x 52 = 312
8 and 39 8 x 39 = 312
12 and 26 12 x 26 = 312
13 and 24 13 x 24 = 312

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 312. They are called negative pair factors.

Hence, the negative pairs of 312 would be ( -1 , -312 ) , ( -2 , -156 ) , ( -3 , -104 ) , ( -4 , -78 ) , ( -6 , -52 ) , ( -8 , -39 ) , ( -12 , -26 ) and ( -13 , -24 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 312 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 312.
• Every number is a factor of zero (0), since 312 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, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are exact divisors of 312.
• Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. Each factor divides 312 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312 are all less than or equal to 312.

• How do you find factors of a negative number? ( eg. -312 )?

Factors of -312 are -1, -2, -3, -4, -6, -8, -12, -13, -24, -26, -39, -52, -78, -104, -156, -312.

• What is the sum of all factors of 312?

The sum of all factors of 312 is 840.

• What is prime factorization of 312?

Prime factorization of 312 is 2 x 2 x 2 x 3 x 13.

• What are the pair factors of 312?

Pair factors of 312 are (1,312), (2,156), (3,104), (4,78), (6,52), (8,39), (12,26), (13,24).

• What are six multiples of 312?

First five multiples of 312 are 624, 936, 1248, 1560, 1872, 2184.

• Is 312 a whole number?

Yes 312 is a whole number.

• Which is the smallest prime factor of 312?

Smallest prime factor of 312 is 2.

• What are five multiples of 312?

First five multiples of 312 are 624, 936, 1248, 1560, 1872.

• Write all factors of 312?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.

#### Examples of Factors

Joey wants to write all the prime factors of 312 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 312 are 2, 2, 2, 3, 13.
So in exponential form it can be written as 23 x 3 x 13.

How many factors are there for 312?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
So there are in total 16 factors.

Kevin has been asked to write 15 factor(s) of 312. Can you predict the answer?

15 factor(s) of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156.

Sammy is puzzled while calculating the prime factors of 312. Can you help him find them?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Prime factors of 312 are 2, 2, 2, 3, 13

What is prime factorization of 312?

Prime factorization of 312 is 2 x 2 x 2 x 3 x 13 = 23 x 3 x 13.

Ariel has been assigned the task to find the product of all the prime factors of 312. Can you help her?

Prime factors of 312 are 2, 2, 2, 3, 13.
Hence, the product of prime factors of 78.

Can you help Rubel to find out the product of the even factors of 312?

Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Even factors of 312 are 2, 4, 6, 8, 12, 24, 26, 52, 78, 104, 156, 312.
Hence, product of even factors of 312 is; 2 x 4 x 6 x 8 x 12 x 24 x 26 x 52 x 78 x 104 x 156 x 312 = 59034724126949380.