The factors of 252can either be prime or composite. Subsequently, 252is 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 252in pairs alongside solved examples for a better understanding.
- Factors of 252: 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
- Prime factorization of 252: 2^{2}× 3^{2}× 7
1. | What Are the Factors of 252? |
2. | How to Calculate Factors of 252? |
3. | Factors of 252by Prime Factorization |
4. | Factors of 252in Pairs |
5. | FAQs on Factors of 252 |
What are the Factors of 252?
A factor is a number thatdivides the given number without leaving a remainder, so the numbers which give the remainder as 0 when divided by 252will be the factors of 252. For Example: 252÷ 2 = 126. Here we get the quotient 126and the remainder is 0. Hence 2 and 126are the factors of 252.
How to Calculate the Factors of 252?
To find the factors of 252we have to find the numbers which when divided by 252give the remainder as 0. We will start dividing 252with 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 = 0 |
252÷ 2 | Remainder = 0 Hence, Factor = 2 |
252÷ 3 | Remainder = 0 |
252÷ 4 | Remainder = 0 |
252÷ 6 | Remainder = 0 |
252÷ 7 | Remainder = 0 |
252÷ 9 | Remainder = 0 |
252÷ 12 | Remainder = 0 |
252÷ 14 | Remainder = 0 |
252÷ 18 | Remainder = 0 |
252÷ 21 | Remainder = 0 Hence, Factor = 21 |
252÷ 28 | Remainder = 0 |
252÷ 36 | Remainder = 0 |
252÷ 42 | Remainder = 0 |
252÷ 63 | Remainder = 0 |
252÷ 84 | Remainder = 0 |
252÷ 126 | Remainder = 0 |
252÷ 252 | Remainder = 0 |
Therefore, the factors of 252are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252.
Explore factors using illustrations and interactive examples
- Factors of 108 – The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
- Factors of 180 – The factors of 280 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
- Factors of 28 – The factors of 28 are 1, 2, 4, 7, 14, 28.
- Factors of 80 – The factors of 80 are 1, 2, 4, 5, 8, 10, 20, 40, 80.
- Factors of 20 – The factors of 20 are 1, 2, 4, 5, 10, 20.
- Factors of 8 – The factors of 8 are 1, 2, 4, 8.
Factors of 252by 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 thequotient as 1.
Division Method
- Step 1. Dividethe number 252with the smallest prime number which gives the remainder as 0.
- Step 2. After dividing 252with its smallest prime factor obtain the quotient.
- Step 3. Repeatstep 1 with the obtained quotient.
Prime factorization of 252
The smallest prime number as a factor of 252is 2. So, dividing 252by 2.
252÷ 2 = 126
Now the quotient is 126with the smallest prime factor as 2.
Now 126÷ 2 = 63
Similarly, 63÷ 3= 21
21÷ 3= 7
7 ÷ 7= 1
So, the prime factorization of 252is. 252= 2 × 2 × 3× 3× 7= 2^{2}× 3^{2}× 7.
Factor Tree Method
The factor tree method can be practiced as shown below
So, the prime factorization of 252is. 252= 2 × 2 × 3× 3× 7= 2^{2}× 3^{2}× 7.
Factors of 252in Pairs
Pair factors of a number imply two numbers whose product will provide the given number. The pair factors of 252will be the pair of numbers whose product will provide 252as result. The table shown below represents the calculation of factors of 252in 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 252would be (-1, -252), (-2, -126), (-3, -84), (-4, -63), (-6, -42), (-7, -36), (-9, -28),(-12, -21) and (-14, -18).
Important Notes
- Factors of a number can only be integers except 0.
- Prime numbers only have two factors 1 and the number itself andcomposite numbers have more than 2 factors and can be represented as the product of two prime numbers.As 252 has more than two factors, this makes it a composite number.
- 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 252should be divided to make it a perfect square?
FAQs on Factors of 252
What are the prime factors of 252?
The factors of 252are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. Thus, theprime factors of 252are, 2, 3,and 7.
Is 252a perfect cube?
Perfect cubes are numbers that can be expressed as a product of the cube of a number. The prime factorization of 252 is given as 252 =2^{2}× 3^{2}×7. We can see that, 252 cannot be expressed as a product of cube of a number. Hence, 252 is not a perfect cube.
What are the odd factors of 252?
The factors of 252are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. The odd factors of 252 are, 3, 7, 9, 21and 63.
What are the negative factors of 252?
The negative factors of 252are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, -252.
How many factors of 252are perfect squares?
The factors of 252are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. Perfect squares among the above factors are 4, 9,and 36.