What are the Factors of 156?
If the number 156 is divided by a natural number such that the remainder is zero, this natural number is known as a factor of 156. Here, the quotient obtained on division is also a factor of 156.
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156 because all these numbers divide the number 156 evenly.
This table describes the factors of 156 in different ways such as a list, factor pairs and in a prime factorization format.
Factor List of 156
Divisibility rules and division facts can be applied to determine the factors of 156.
We can stop the derivation of factors with this step because the multiplication equations start to repeat. So, the factors of 156 are the multiplicands of each multiplication equation. Since there are 6 multiplication equations with unique multiplicands, the number 156 has twelve factors, which are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
Prime factorization of 156
Prime factorization implies that we express a number as a product of prime numbers. The prime numbers multiplied here are known as the prime factors of the original number.
The factor tree of 156 represents the prime factorization of 156.
Therefore the prime factorization of 156 are, 2 x 2 x 3 x 13 and the prime factors of 156 are, 2 , 3 and 13.
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Factor pairs of 156
A factor pair of 156 is a set of any of its two factors whose product is 156. The factor pairs of a number can be written from the list of factors of that number.
The factor pairs of 156 are listed in the table.
Solved Factors of 156 Examples
Example 1: Find the factors common between 156 and 38.
Solution:
Factors of 156 = 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
Factors of 38 = 1, 2, 19 and 38
Therefore, the factors common between 156 and 38 are 1 and 2.
Example 2: Find the greatest common factor of 156 and 289.
Solution:
Factors of 156 = 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78 and 156.
Factors of 289 = 1, 17, and 289.
So, the only common factor of 156 and 289 is 1.
Therefore, the greatest common factor of 156 and 289 is 1.
Example 3: Stacy has 156 marbles with her and she decides to divide them among her 6 friends. How can she divide the marbles equally?
Solution:
Let us divide 156 by 6, that is,
156 ÷ 6
= 26 (6, 26) is a factor pair of 156, that is, 6 x 26 = 156.
Therefore Stacy can divide 156 marbles equally among her 6 friends by giving each friend 26 marbles.
The negative factor pairs of 156 are (-1, -156), (-2, -78), (-3, -52), (-4, -39), (-6, -26) and (-12, -13).
The division of any number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all numbers.
Yes, 26 is a factor of 156. As 26 divides 156 exactly, giving us 6 as the quotient and without leaving any remainder.
156 has more than two factors. This shows us that 156 is not a prime number.