Last updated on May 26th, 2025
In mathematics, there are lots of numbers that when divided by other numbers leave no remainder, these numbers are called factors. We use it in our vehicles mileage and money handling. Now, we’ll learn what factors are and factors of 156 let us now see.
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.
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).
It is very normal to make mistakes when learning to find the factors. Here are the commonly made mistakes by children. Avoid these when practising!
A bookshelf is 156 cm long. If each shelf is 13 cm wide, how many shelves can fit?
You can fit 12 shelves, as 156÷13=12.
To find out how many shelves fit, divide the shelf length (156 cm) by each shelf's width (13 cm).
If the area of a square is 156 square units, what is the length of one side?
The side length is √156= 12.49 units because the area of a square is the side length squared.
To find the side, we take the square root of the area (√156) since area = side × side.
If the perimeter of a rectangle is 156 units, and its length is 52 units, what is its width?
The width is 26 units, calculated by (156−2×52)/2=26.
Subtract twice the length (2 × 52 = 104) from the perimeter (156). Then divide by 2: (156–104) ÷ 2 = 26.
A group of 156 people is divided into teams of 13. How many teams are there?
There are 12 teams because 156÷13=12.
To find the number of teams, divide the total number of people (156) by the number of people per team (13).
A book weighs 156 grams. If 12 books are placed together, what is their total weight?
The total weight is 1872 grams because 156×12=1872.
Multiply the weight of one book (156 grams) by 12 to find the total weight of all 12 books.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.