Factors Of 156

We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 156 has more than 2 factors. Let us find what the factors are.

Negative factors of 156: -1, -2, -3, -4, -6, -12, -13, -26, -39, -52, -78, and -156.

Prime factors of 156: The prime factors of 156 are 2, 3, and 13.

Prime factorization of 156: 2×2×3×13

The sum of factors of 156: 1+2+3+4+6+12+13+26+39+52+78+156= 392
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 156.

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 156. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 156.

Step 2: These numbers will be called the factors of 156.

Step 3: Students have to write these pairs of numbers for this method.

List of numbers whose product is 156

156 × 1= 156

78 × 2= 156

52×3= 156

39×4= 156

26×6= 156

13×12= 156

So the pair of numbers whose product is 156 are (1,156), (78,2), (52,3), (39,4), (26,6) and (13,12).
 

For the division method, the process of division will go on until the remainder becomes zero.

Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 156÷1 = 156

Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 156÷2 = 78 and so on.

Prime factorization is the process where the number will be a product of prime factors or prime numbers.

The prime factors of 156 are 2, 3, and 13. We find the prime factors of 156 by two ways.

By Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 156, the steps are like this:

156/2= 78

78/2= 39

39/3= 13

13/13= 13

As 13 is a prime number, it is only divisible by 13. Hence, The prime factorization of the number 156 is 2×2×2×13.
 

This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.

Step 1: 156 divided by 2 gives us the answer being 78.

Step 2: 78 divided by 2 gives us 39.

Step 3: Again, we break 39 by 3, and we get 13 as our answer for 39. 

Step 4: This we can’t divide further into, since 13 is a prime number. 

There are positive and negative factor pairs for a given number. Let us look at these factor pairs.

Positive Factor Pairs: (1,156), (78,2), (52,3), (39,4), (26,6) and (13,12).

Negative Factor Pairs: (-1,-156), (-78,-2), (-52,-3), (-39,-4), (-26,-6) and (-13,-12).
 

• Factors: Whole numbers that can be multiplied together to yield a given number. For example, the factors of 156 include numbers like 1, 2, and 3, which divide 156 evenly without leaving a remainder.

• Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, and 7.

• Remainder: The amount left over when one number is divided by another. If a number is completely divisible, the remainder is zero.