# Factors of 1356

Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, and 1356

#### How to find factors of a number

 1.   Find factors of 1356 using Division Method 2.   Find factors of 1356 using Prime Factorization 3.   Find factors of 1356 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 1356

• Divide 1356 by 1: 1356 ÷ 1 : Remainder = 0
• Divide 1356 by 2: 1356 ÷ 2 : Remainder = 0
• Divide 1356 by 3: 1356 ÷ 3 : Remainder = 0
• Divide 1356 by 4: 1356 ÷ 4 : Remainder = 0
• Divide 1356 by 6: 1356 ÷ 6 : Remainder = 0
• Divide 1356 by 12: 1356 ÷ 12 : Remainder = 0
• Divide 1356 by 113: 1356 ÷ 113 : Remainder = 0
• Divide 1356 by 226: 1356 ÷ 226 : Remainder = 0
• Divide 1356 by 339: 1356 ÷ 339 : Remainder = 0
• Divide 1356 by 452: 1356 ÷ 452 : Remainder = 0
• Divide 1356 by 678: 1356 ÷ 678 : Remainder = 0
• Divide 1356 by 1356: 1356 ÷ 1356 : Remainder = 0

Hence, Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, and 1356

#### 2. Steps to find factors of 1356 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 1356 using the division method, follow these steps:

• Step 1. Start dividing 1356 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 1356, which is 2. Divide 1356 by 2 to obtain the quotient (678).
1356 ÷ 2 = 678
• Step 3. Repeat step 1 with the obtained quotient (678).
678 ÷ 2 = 339
339 ÷ 3 = 113
113 ÷ 113 = 1

So, the prime factorization of 1356 is, 1356 = 2 x 2 x 3 x 113.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 1356 as shown below:

So, the prime factorization of 1356 is, 1356 = 2 x 2 x 3 x 113.

#### 3. Find factors of 1356 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 1356 would be the two numbers which, when multiplied, give 1356 as the result.

The following table represents the calculation of factors of 1356 in pairs:

Factor Pair Pair Factorization
1 and 1356 1 x 1356 = 1356
2 and 678 2 x 678 = 1356
3 and 452 3 x 452 = 1356
4 and 339 4 x 339 = 1356
6 and 226 6 x 226 = 1356
12 and 113 12 x 113 = 1356

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 1356. They are called negative pair factors.

Hence, the negative pairs of 1356 would be ( -1 , -1356 ) , ( -2 , -678 ) , ( -3 , -452 ) , ( -4 , -339 ) , ( -6 , -226 ) and ( -12 , -113 ) .

#### 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. 1356 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 1356.
• Every number is a factor of zero (0), since 1356 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, 113, 226, 339, 452, 678, 1356 are exact divisors of 1356.
• Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356. Each factor divides 1356 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356 are all less than or equal to 1356.

• How do you find factors of a negative number? ( eg. -1356 )?

Factors of -1356 are -1, -2, -3, -4, -6, -12, -113, -226, -339, -452, -678, -1356.

• What is the sum of all factors of 1356?

The sum of all factors of 1356 is 3192.

• What is prime factorization of 1356?

Prime factorization of 1356 is 2 x 2 x 3 x 113.

• What are the pair factors of 1356?

Pair factors of 1356 are (1,1356), (2,678), (3,452), (4,339), (6,226), (12,113).

• What are six multiples of 1356?

First five multiples of 1356 are 2712, 4068, 5424, 6780, 8136, 9492.

• Is 1356 a whole number?

Yes 1356 is a whole number.

• Which is the smallest prime factor of 1356?

Smallest prime factor of 1356 is 2.

• What are five multiples of 1356?

First five multiples of 1356 are 2712, 4068, 5424, 6780, 8136.

• Write all factors of 1356?

Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356.

#### Examples of Factors

Joey wants to write all the prime factors of 1356 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 1356 are 2, 2, 3, 113.
So in exponential form it can be written as 22 x 3 x 113.

How many factors are there for 1356?

Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356.
So there are in total 12 factors.

Kevin has been asked to write 11 factor(s) of 1356. Can you predict the answer?

11 factor(s) of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678.

Sammy is puzzled while calculating the prime factors of 1356. Can you help him find them?

Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356.
Prime factors of 1356 are 2, 2, 3, 113

What is prime factorization of 1356?

Prime factorization of 1356 is 2 x 2 x 3 x 113 = 22 x 3 x 113.

Ariel has been assigned the task to find the product of all the prime factors of 1356. Can you help her?

Prime factors of 1356 are 2, 2, 3, 113.
Hence, the product of prime factors of 678.

Can you help Rubel to find out the product of the even factors of 1356?

Factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356.
Even factors of 1356 are 2, 4, 6, 12, 226, 452, 678, 1356.
Hence, product of even factors of 1356 is; 2 x 4 x 6 x 12 x 226 x 452 x 678 x 1356 = 54095201243136.