Factors of 252

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.

• 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: 2² × 3² × 7

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.

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.

Therefore, the factors of 252 are 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.

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 2. After dividing 252 with its smallest prime factor obtain the quotient.
• 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 = 21
21 ÷ 3 = 7
7 ÷ 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.

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:

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).

• Factors of a number can only be integers except 0.
• Prime numbers only have two factors 1 and the number itself and composite 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. 
•  

• 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?

What are the prime factors of 252?

The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252. Thus, the prime factors of 252 are, 2, 3, and 7.

Is 252 a 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 = 2² × 3² × 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 252 are 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, 21 and 63.

What are the negative factors of 252?

The negative factors of 252 are -1, -2, -3, -4, -6, -7, -9, -12, -14, -18, -21, -28, -36, -42, -63, -84, -126, -252.

How many factors of 252 are perfect squares?

The factors of 252 are 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.