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 816

Factors of 816 are numbers that, when multiplied in pairs give the product as 816. It has total 20 factors of which 816 is the biggest factor and the prime factors of 816 are 2, 3, 17. The Prime Factorization of 816 is 24 × 31 × 171.

  • All Factors of 816: 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408 and 816
  • Prime Factors of 816: 2, 3, 17
  • Prime Factorization of 816: 24 × 31 × 171
  • Sum of Factors of 816: 2232
1. What Are the Factors of 816?
2. Factors of 816 by Prime Factorization
3. Factors of 816 in Pairs
4. FAQs on Factors of 816
Factors of 816

What are Factors of 816?

Factors of 816 are pairs of those numbers whose products result in 816. These factors are either prime numbers or composite numbers.

How to Find the Factors of 816?

To find the factors of 816, we will have to find the list of numbers that would divide 816 without leaving any remainder.

  • 816/34 = 24; therefore, 34 is a factor of 816 and 24 is also a factor of 816.
  • 816/2 = 408; therefore, 2 is a factor of 816 and 408 is also a factor of 816.
Similarly we can find other factors. Hence, the factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816.

☛ Also Check:

Factors of 816 by Prime Factorization

The number 816 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 816. The first step is to divide the number 816 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 816 ÷ 2 = 408
  • 408 ÷ 2 = 204
  • 204 ÷ 2 = 102
  • 102 ÷ 2 = 51

Further dividing 51 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 51 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 816 can be written as 24 × 31 × 171 where 2, 3, 17 are prime.

 

Factors of 816 in Pairs

Pair factors of 816 are the pairs of numbers that when multiplied give the product 816. The factors of 816 in pairs are:

  • 1 × 816 = (1, 816)
  • 2 × 408 = (2, 408)
  • 3 × 272 = (3, 272)
  • 4 × 204 = (4, 204)
  • 6 × 136 = (6, 136)
  • 8 × 102 = (8, 102)
  • 12 × 68 = (12, 68)
  • 16 × 51 = (16, 51)
  • 17 × 48 = (17, 48)
  • 24 × 34 = (24, 34)

Negative pair factors of 816 are:

  • -1 × -816 = (-1, -816)
  • -2 × -408 = (-2, -408)
  • -3 × -272 = (-3, -272)
  • -4 × -204 = (-4, -204)
  • -6 × -136 = (-6, -136)
  • -8 × -102 = (-8, -102)
  • -12 × -68 = (-12, -68)
  • -16 × -51 = (-16, -51)
  • -17 × -48 = (-17, -48)
  • -24 × -34 = (-24, -34)

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

Factors of 816 Solved Examples

  1. Example 1: How many factors are there for 816?

    Solution:

    The factors of 816 are too many, therefore if we can find the prime factorization of 816, 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 816 = 24 × 31 × 171
    Therefore, the total number of factors are (4 + 1) × (1 + 1) × (1 + 1) = 5 × 2 × 2 = 20

  2. Example 2: Find the LCM and Highest Common Factor (HCF) of 816 and 150.

    Solution:

    The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816 and factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150.

    Therefore, the LCM of 816 and 150 is 20400 and Highest Common Factor (HCF) of 816 and 150 is 6.

  3. Example 3: Find if 1, 4, 8, 16, 51, 267, 408 and 816 are factors of 816.

    Solution:

    When we divide 816 by 267 it leaves a remainder. Therefore, the number 267 is not a factor of 816. All numbers except 267 are factors of 816.

  4. Example 4: Find the product of all the prime factors of 816.

    Solution:

    Since, the prime factors of 816 are 2, 3, 17. Therefore, the product of prime factors = 2 × 3 × 17 = 102.

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 816

What are the Factors of 816?

The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816 and its negative factors are -1, -2, -3, -4, -6, -8, -12, -16, -17, -24, -34, -48, -51, -68, -102, -136, -204, -272, -408, -816.

What is the Sum of Factors of 816?

Sum of all factors of 816 = (24 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (171 + 1 - 1)/(17 - 1) = 2232

What are the Prime Factors of 816?

The prime factors of 816 are 2, 3, 17.

What is the Greatest Common Factor of 816 and 677?

The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816 and the factors of 677 are 1, 677. 816 and 677 have only one common factor which is 1. This implies that 816 and 677 are co-prime.

Hence, the Greatest Common Factor (GCF) of 816 and 677 is 1.

What are the Common Factors of 816 and 762?

Since, the factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816 and the factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762.
Hence, [1, 2, 3, 6] are the common factors of 816 and 762.

Math worksheets and
visual curriculum