Last updated on May 26th, 2025
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 972, how they are used in real life, and tips to learn them quickly.
The numbers that divide 972 evenly are known as factors of 972.
A factor of 972 is a number that divides the number without remainder.
The factors of 972 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, and 972.
Negative factors of 972: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, -243, -324, -486, and -972.
Prime factors of 972: 2 and 3.
Prime factorization of 972: 2² × 3â”.
The sum of factors of 972: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 243 + 324 + 486 + 972 = 3,234
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 972. Identifying the numbers which are multiplied to get the number 972 is the multiplication method.
Step 1: Multiply 972 by 1, 972 × 1 = 972.
Step 2: Check for other numbers that give 972 after multiplying
2 × 486 = 972
3 × 324 = 972
4 × 243 = 972
6 × 162 = 972
9 × 108 = 972
12 × 81 = 972
18 × 54 = 972
27 × 36 = 972
Therefore, the positive factor pairs of 972 are: (1, 972), (2, 486), (3, 324), (4, 243), (6, 162), (9, 108), (12, 81), (18, 54), (27, 36).
All these factor pairs result in 972.
For every positive factor, there is a negative factor.
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 972 by 1, 972 ÷ 1 = 972.
Step 2: Continue dividing 972 by the numbers until the remainder becomes 0.
972 ÷ 1 = 972
972 ÷ 2 = 486
972 ÷ 3 = 324
972 ÷ 4 = 243
972 ÷ 6 = 162
972 ÷ 9 = 108
972 ÷ 12 = 81
972 ÷ 18 = 54
972 ÷ 27 = 36
Therefore, the factors of 972 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 972.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
Using Prime Factorization: In this process, prime factors of 972 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
972 ÷ 2 = 486
486 ÷ 2 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 972 are 2 and 3.
The prime factorization of 972 is: 2² × 3â”.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 972 is divided by 2 to get 486.
Step 2: Now divide 486 by 2 to get 243.
Step 3: Then divide 243 by 3 to get 81.
Step 4: Divide 81 by 3 to get 27.
Step 5: Divide 27 by 3 to get 9.
Step 6: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 972 is: 2² × 3â”.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 972: (1, 972), (2, 486), (3, 324), (4, 243), (6, 162), (9, 108), (12, 81), (18, 54), (27, 36).
Negative factor pairs of 972: (-1, -972), (-2, -486), (-3, -324), (-4, -243), (-6, -162), (-9, -108), (-12, -81), (-18, -54), (-27, -36).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 18 friends and 972 candies. How will they divide it equally?
They will get 54 candies each.
To divide the candies equally, we need to divide the total candies with the number of friends.
972/18 = 54
A rectangular garden has a length of 27 meters and a total area of 972 square meters. Find the width?
36 meters.
To find the width of the garden, we use the formula,
Area = length × width
972 = 27 × width
To find the value of width, we need to shift 27 to the left side.
972/27 = width
Width = 36.
There are 81 gift boxes and 972 candies. How many candies will be in each gift box?
Each gift box will have 12 candies.
To find the candies in each gift box, divide the total candies with the gift boxes.
972/81 = 12
In a theater, there are 972 seats and 9 rows. How many seats are there in each row?
There are 108 seats in each row.
Dividing the seats by the total rows, we will get the number of seats in each row.
972/9 = 108
972 apples need to be arranged in 4 baskets. How many apples will go into each basket?
Each of the baskets has 243 apples.
Divide total apples with baskets.
972/4 = 243
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.