A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

 

Factors of 396

Factors of 396 are integers that can be divided evenly into 396. It has total 18 factors of which 396 is the biggest factor and the prime factors of 396 are 2, 3, 11. The sum of all factors of 396 is 1092.

  • All Factors of 396: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198 and 396
  • Prime Factors of 396: 2, 3, 11
  • Prime Factorization of 396: 22 × 32 × 111
  • Sum of Factors of 396: 1092
1. What Are the Factors of 396?
2. Factors of 396 by Prime Factorization
3. Factors of 396 in Pairs
4. FAQs on Factors of 396
Factors of 396

What are Factors of 396?

Factors of 396 are pairs of those numbers whose products result in 396. These factors are either prime numbers or composite numbers.

How to Find the Factors of 396?

To find the factors of 396, we will have to find the list of numbers that would divide 396 without leaving any remainder.

  • 396/396 = 1; therefore, 396 is a factor of 396.
  • 396/11 = 36; therefore, 11 is a factor of 396.
Similarly we can find other factors. Hence, the factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396.

☛ Also Check:

Factors of 396 by Prime Factorization

The number 396 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 396. The first step is to divide the number 396 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 396 ÷ 2 = 198
  • 198 ÷ 2 = 99

Further dividing 99 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 99 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 396 can be written as 22 × 32 × 111 where 2, 3, 11 are prime.

 

Factors of 396 in Pairs

Pair factors of 396 are the pairs of numbers that when multiplied give the product 396. The factors of 396 in pairs are:

  • 1 × 396 = (1, 396)
  • 2 × 198 = (2, 198)
  • 3 × 132 = (3, 132)
  • 4 × 99 = (4, 99)
  • 6 × 66 = (6, 66)
  • 9 × 44 = (9, 44)
  • 11 × 36 = (11, 36)
  • 12 × 33 = (12, 33)
  • 18 × 22 = (18, 22)

Negative pair factors of 396 are:

  • -1 × -396 = (-1, -396)
  • -2 × -198 = (-2, -198)
  • -3 × -132 = (-3, -132)
  • -4 × -99 = (-4, -99)
  • -6 × -66 = (-6, -66)
  • -9 × -44 = (-9, -44)
  • -11 × -36 = (-11, -36)
  • -12 × -33 = (-12, -33)
  • -18 × -22 = (-18, -22)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 396 Solved Examples

  1. Example 1: How many factors are there for 396?

    Solution:

    The factors of 396 are too many, therefore if we can find the prime factorization of 396, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 396 = 22 × 32 × 111
    Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 396 and 56.

    Solution:

    The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 and factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.

    Therefore, the Least Common Multiple (LCM) of 396 and 56 is 5544 and Highest Common Factor (HCF) of 396 and 56 is 4.

  3. Example 3: Find if 4, 12, 18, 33, 36, 66, 99 and 322 are factors of 396.

    Solution:

    When we divide 396 by 322 it leaves a remainder. Therefore, the number 322 is not a factor of 396. All numbers except 322 are factors of 396.

  4. Example 4: Find the product of all the prime factors of 396.

    Solution:

    Since, the prime factors of 396 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.

Show Solution >

go to slidego to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

 

FAQs on Factors of 396

What are the Factors of 396?

The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 and its negative factors are -1, -2, -3, -4, -6, -9, -11, -12, -18, -22, -33, -36, -44, -66, -99, -132, -198, -396.

What is the Sum of all Factors of 396?

Sum of all factors of 396 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) = 1092

What are the Prime Factors of 396?

The prime factors of 396 are 2, 3, 11.

What is the Greatest Common Factor of 396 and 132?

The factors of 396 and 132 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 and 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 respectively.

Common factors of 396 and 132 are [1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132].

Hence, the Greatest Common Factor (GCF) of 396 and 132 is 132.

How Many Factors of 396 are also Factors of 126?

Since, the factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396 and the factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Hence, [1, 2, 3, 6, 9, 18] are the common factors of 396 and 126.

Math worksheets and
visual curriculum