The factors of 252 can either be prime or composite. Subsequently, 252 is an even composite number itself which comprises of factors that are either prime or composite. How about we figure out how to compute the factors of 252, prime factors of 252, and factors of 252 in pairs alongside solved examples for a better understanding.
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1. | What Are the Factors of 252? |
2. | How to Calculate Factors of 252? |
3. | Factors of 252 by Prime Factorization |
4. | Factors of 252 in Pairs |
5. | FAQs on Factors of 252 |
What are the Factors of 252?
A factor is a number that divides the given number without leaving a remainder, so the numbers which give the remainder as 0 when divided by 252 will be the factors of 252. For Example: 252 ÷ 2 = 126. Here we get the quotient 126 and the remainder is 0. Hence 2 and 126 are the factors of 252.
How to Calculate the Factors of 252?
To find the factors of 252 we have to find the numbers which when divided by 252 give the remainder as 0. We will start dividing 252 with Natural numbers i.e., 1, 2, 3, …. Up to 126 (Half of 252). So, all the numbers which will provide the remainder as 0 will be the factors of 252. This method is known as Division Method. The table below provides the representation of the above method.
Division | Factor |
252 ÷ 1 | Remainder = 0Hence, Factor = 1 |
252 ÷ 2 | Remainder = 0 Hence, Factor = 2 |
252 ÷ 3 | Remainder = 0Hence, Factor = 3 |
252 ÷ 4 | Remainder = 0Hence, Factor = 4 |
252 ÷ 6 | Remainder = 0Hence, Factor = 6 |
252 ÷ 7 | Remainder = 0Hence, Factor = 7 |
252 ÷ 9 | Remainder = 0Hence, Factor = 9 |
252 ÷ 12 | Remainder = 0Hence, Factor = 12 |
252 ÷ 14 | Remainder = 0Hence, Factor = 14 |
252 ÷ 18 | Remainder = 0Hence, Factor = 18 |
252 ÷ 21 | Remainder = 0 Hence, Factor = 21 |
252 ÷ 28 | Remainder = 0Hence, Factor = 4 |
252 ÷ 36 | Remainder = 0Hence, Factor = 36 |
252 ÷ 42 | Remainder = 0Hence, Factor = 42 |
252 ÷ 63 | Remainder = 0Hence, Factor = 63 |
252 ÷ 84 | Remainder = 0Hence, Factor = 84 |
252 ÷ 126 | Remainder = 0Hence, Factor = 126 |
252 ÷ 252 | Remainder = 0Hence, Factor = 252 |
Therefore, the factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
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Factors of 252 by Prime Factorization
Prime factorization is a method of converting any composite number into the product of its prime factors. We will divide the number with subsequent prime numbers until we get the quotient as 1.
Division Method
Step 1. Divide the number 252 with the smallest prime number which gives the remainder as 0.Step 3. Repeat step 1 with the obtained quotient.Prime factorization of 252
The smallest prime number as a factor of 252 is 2. So, dividing 252 by 2.
252 ÷ 2 = 126
Now the quotient is 126 with the smallest prime factor as 2.
Now 126 ÷ 2 = 63
Similarly, 63 ÷ 3 = 2121 ÷ 3 = 77 ÷ 7 = 1
So, the prime factorization of 252 is. 252 = 2 × 2 × 3 × 3 × 7 = 22 × 32 × 7.
Factor Tree Method
The factor tree method can be practiced as shown below
So, the prime factorization of 252 is. 252 = 2 × 2 × 3 × 3 × 7 = 22 × 32 × 7.
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Factors of 252 in Pairs
Pair factors of a number imply two numbers whose product will provide the given number. The pair factors of 252 will be the pair of numbers whose product will provide 252 as result. The table shown below represents the calculation of factors of 252 in pairs:
Factor pair | Pair factorization |
1 and 252 | 1 × 252 = 252 |
2 and 126 | 2 × 126 = 252 |
3 and 84 | 3 × 84 = 252 |
4 and 63 | 4 × 63 = 252 |
6 and 42 | 6 × 42 = 252 |
7 and 36 | 7 × 36 = 252 |
9 and 28 | 9 × 28 = 252 |
12 and 21 | 12 × 21 = 252 |
14 and 18 | 14 × 18 = 252 |
Also, the product of two negative numbers results in a positive number. So, the product of negative values of the above factors pairs will result in 252. They are known as negative pair factors. Hence, the negative factor pairs of 252 would be (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28), (-12, -21) and (-14, -18).
Important Notes
As the sum of digits of 252 is 9, it is divisible by 3 as well as 9. Hence, 3 and 9 are factors of 252.
Challenging Questions:
What is the mean of all the even factors of 252?Using prime factorization, find the number by which 252 should be divided to make it a perfect square?