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 the items equally, arranging things, etc. In this topic, we will learn about the factors of 252, how they are used in real life, and the tips to learn them quickly.
The numbers that divide 252 evenly are known as factors of 252.
A factor of 252 is a number that divides the number without remainder.
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.
Negative factors of 252: -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, and -252.
Prime factors of 252: 2, 3, and 7.
Prime factorization of 252: 2² × 3² × 7.
The sum of factors of 252: 1 + 2 + 3 + 4 + 6 + 7 + 9 + 12 + 14 + 18 + 21 + 28 + 36 + 42 + 63 + 84 + 126 + 252 = 768.
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 252. Identifying the numbers which are multiplied to get the number 252 is the multiplication method.
Step 1: Multiply 252 by 1, 252 × 1 = 252.
Step 2: Check for other numbers that give 252 after multiplying
2 × 126 = 252
3 × 84 = 252
4 × 63 = 252
6 × 42 = 252
7 × 36 = 252
9 × 28 = 252
12 × 21 = 252
14 × 18 = 252
Therefore, the positive factor pairs of 252 are: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18). For every positive factor, there is a negative factor.
Dividing the given numbers with the 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 the simple division method -
Step 1: Divide 252 by 1, 252 ÷ 1 = 252.
Step 2: Continue dividing 252 by the numbers until the remainder becomes 0.
252 ÷ 1 = 252
252 ÷ 2 = 126
252 ÷ 3 = 84
252 ÷ 4 = 63
252 ÷ 6 = 42
252 ÷ 7 = 36
252 ÷ 9 = 28
252 ÷ 12 = 21
252 ÷ 14 = 18
Therefore, the factors of 252 are: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
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 252 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
The prime factors of 252 are 2, 3, and 7.
The prime factorization of 252 is: 2² × 3² × 7.
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 252 is divided by 2 to get 126.
Step 2: Now divide 126 by 2 to get 63.
Step 3: Then divide 63 by 3 to get 21.
Step 4: Divide 21 by 3 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 252 is: 2² × 3² × 7.
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 252: (1, 252), (2, 126), (3, 84), (4, 63), (6, 42), (7, 36), (9, 28), (12, 21), (14, 18).
Negative factor pairs of 252: (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28), (-12, -21), (-14, -18).
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 9 students and 252 candies. How will they divide it equally?
They will get 28 candies each.
To divide the candies equally, we need to divide the total candies with the number of students.
252/9 = 28
A rectangular garden has a length of 14 meters and the total area is 252 square meters. Find the width.
18 meters.
To find the width of the garden, we use the formula,
Area = length × width
252 = 14 × width
To find the value of width, we need to shift 14 to the left side.
252/14 = width
Width = 18.
There are 21 gift bags and 252 chocolates. How many chocolates will be in each bag?
Each bag will have 12 chocolates.
To find the chocolates in each bag, divide the total chocolates with the bags.
252/21 = 12
In a class, there are 252 students, and 7 groups. How many students are there in each group?
There are 36 students in each group.
Dividing the students with the total groups, we will get the number of students in each group.
252/7 = 36
252 books need to be arranged in 6 shelves. How many books will go on each shelf?
Each of the shelves has 42 books.
Divide total books with shelves.
252/6 = 42
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.