Factors of 1356
Factors of 1356 are numbers that, when multiplied in pairs give the product as 1356. There are overall 12 factors of 1356 among which 1356 is the biggest factor and 2, 3, 113 are its prime factors. The Prime Factorization of 1356 is 2^{2} × 3^{1} × 113^{1}.
 All Factors of 1356: 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678 and 1356
 Prime Factors of 1356: 2, 3, 113
 Prime Factorization of 1356: 2^{2} × 3^{1} × 113^{1}
 Sum of Factors of 1356: 3192
1.  What Are the Factors of 1356? 
2.  Factors of 1356 by Prime Factorization 
3.  Factors of 1356 in Pairs 
4.  FAQs on Factors of 1356 
What are Factors of 1356?
Factors of 1356 are pairs of those numbers whose products result in 1356. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1356?
To find the factors of 1356, we will have to find the list of numbers that would divide 1356 without leaving any remainder.
 1356/113 = 12; therefore, 113 is a factor of 1356 and 12 is also a factor of 1356.
 1356/339 = 4; therefore, 339 is a factor of 1356 and 4 is also a factor of 1356.
☛ Also Check:
 Factors of 20  The factors of 20 are 1, 2, 4, 5, 10, 20
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 Factors of 14  The factors of 14 are 1, 2, 7, 14
 Factors of 65  The factors of 65 are 1, 5, 13, 65
 Factors of 144  The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 1356 by Prime Factorization
 1356 ÷ 2 = 678
 678 ÷ 2 = 339
Further dividing 339 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 339 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 1356 can be written as 2^{2} × 3^{1} × 113^{1} where 2, 3, 113 are prime.
Factors of 1356 in Pairs
Pair factors of 1356 are the pairs of numbers that when multiplied give the product 1356. The factors of 1356 in pairs are:
 1 × 1356 = (1, 1356)
 2 × 678 = (2, 678)
 3 × 452 = (3, 452)
 4 × 339 = (4, 339)
 6 × 226 = (6, 226)
 12 × 113 = (12, 113)
Negative pair factors of 1356 are:
 1 × 1356 = (1, 1356)
 2 × 678 = (2, 678)
 3 × 452 = (3, 452)
 4 × 339 = (4, 339)
 6 × 226 = (6, 226)
 12 × 113 = (12, 113)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 1356 Solved Examples

Example 1: How many factors are there for 1356?
Solution:
The factors of 1356 are too many, therefore if we can find the prime factorization of 1356, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^{x} × b^{y} × c^{z} where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 1356 = 2^{2} × 3^{1} × 113^{1}
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1356 and 476.
Solution:
The factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356 and factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, 476.
Therefore, the Lowest Common Multiple (LCM) of 1356 and 476 is 161364 and Greatest Common Divisor (GCD) of 1356 and 476 is 4. 
Example 3: Find if 3, 4, 6, 12, 113, 339 and 1193 are factors of 1356.
Solution:
When we divide 1356 by 1193 it leaves a remainder. Therefore, the number 1193 is not a factor of 1356. All numbers except 1193 are factors of 1356.

Example 4: Find the product of all the prime factors of 1356.
Solution:
Since, the prime factors of 1356 are 2, 3, 113. Therefore, the product of prime factors = 2 × 3 × 113 = 678.
FAQs on Factors of 1356
What are the Factors of 1356?
The factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356 and its negative factors are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356.
What is the Sum of the Factors of 1356?
Sum of all factors of 1356 = (2^{2 + 1}  1)/(2  1) × (3^{1 + 1}  1)/(3  1) × (113^{1 + 1}  1)/(113  1) = 3192
What Numbers are the Prime Factors of 1356?
The prime factors of 1356 are 2, 3, 113.
What is the Greatest Common Factor of 1356 and 23?
The factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356 and the factors of 23 are 1, 23. 1356 and 23 have only one common factor which is 1. This implies that 1356 and 23 are coprime.
Hence, the Greatest Common Factor (GCF) of 1356 and 23 is 1.
How Many Factors of 1356 are also Factors of 307?
Since, the factors of 1356 are 1, 2, 3, 4, 6, 12, 113, 226, 339, 452, 678, 1356 and factors of 307 are 1, 307. Hence, 1356 and 307 have only one common factor which is 1. Therefore, 1356 and 307 are coprime.
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