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Factors of 828

Factors of 828 are integers that can be divided evenly into 828. There are overall 18 factors of 828 among which 828 is the biggest factor and 2, 3, 23 are its prime factors. The sum of all factors of 828 is 2184.

  • All Factors of 828: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414 and 828
  • Prime Factors of 828: 2, 3, 23
  • Prime Factorization of 828: 22 × 32 × 231
  • Sum of Factors of 828: 2184
1. What Are the Factors of 828?
2. Factors of 828 by Prime Factorization
3. Factors of 828 in Pairs
4. FAQs on Factors of 828
Factors of 828

What are Factors of 828?

Factors of 828 are pairs of those numbers whose products result in 828. These factors are either prime numbers or composite numbers.

How to Find the Factors of 828?

To find the factors of 828, we will have to find the list of numbers that would divide 828 without leaving any remainder.

  • 828/12 = 69; therefore, 12 is a factor of 828 and 69 is also a factor of 828.
  • 828/36 = 23; therefore, 36 is a factor of 828 and 23 is also a factor of 828.
Similarly we can find other factors. Hence, the factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828.

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Factors of 828 by Prime Factorization

The number 828 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 828. The first step is to divide the number 828 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 828 ÷ 2 = 414
  • 414 ÷ 2 = 207

Further dividing 207 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 207 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 828 can be written as 22 × 32 × 231 where 2, 3, 23 are prime.

 

Factors of 828 in Pairs

Pair factors of 828 are the pairs of numbers that when multiplied give the product 828. The factors of 828 in pairs are:

  • 1 × 828 = (1, 828)
  • 2 × 414 = (2, 414)
  • 3 × 276 = (3, 276)
  • 4 × 207 = (4, 207)
  • 6 × 138 = (6, 138)
  • 9 × 92 = (9, 92)
  • 12 × 69 = (12, 69)
  • 18 × 46 = (18, 46)
  • 23 × 36 = (23, 36)

Negative pair factors of 828 are:

  • -1 × -828 = (-1, -828)
  • -2 × -414 = (-2, -414)
  • -3 × -276 = (-3, -276)
  • -4 × -207 = (-4, -207)
  • -6 × -138 = (-6, -138)
  • -9 × -92 = (-9, -92)
  • -12 × -69 = (-12, -69)
  • -18 × -46 = (-18, -46)
  • -23 × -36 = (-23, -36)

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

Factors of 828 Solved Examples

  1. Example 1: How many factors are there for 828?

    Solution:

    The factors of 828 are too many, therefore if we can find the prime factorization of 828, 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 828 = 22 × 32 × 231
    Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) = 3 × 3 × 2 = 18

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 828 and 312.

    Solution:

    The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 and factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.

    Therefore, the Lowest Common Multiple (LCM) of 828 and 312 is 21528 and Greatest Common Divisor (GCD) of 828 and 312 is 12.

  3. Example 3: Find if 2, 18, 36, 46, 138, 276, 414 and 643 are factors of 828.

    Solution:

    When we divide 828 by 643 it leaves a remainder. Therefore, the number 643 is not a factor of 828. All numbers except 643 are factors of 828.

  4. Example 4: Find the product of all the prime factors of 828.

    Solution:

    Since, the prime factors of 828 are 2, 3, 23. Therefore, the product of prime factors = 2 × 3 × 23 = 138.

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FAQs on Factors of 828

What are the Factors of 828?

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 and its negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -23, -36, -46, -69, -92, -138, -207, -276, -414, -828.

What is the Sum of the Factors of 828?

Sum of all factors of 828 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (231 + 1 - 1)/(23 - 1) = 2184

What are the Pair Factors of 828?

The pair factors of 828 are (1, 828), (2, 414), (3, 276), (4, 207), (6, 138), (9, 92), (12, 69), (18, 46), (23, 36).

What is the Greatest Common Factor of 828 and 775?

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 and the factors of 775 are 1, 5, 25, 31, 155, 775. 828 and 775 have only one common factor which is 1. This implies that 828 and 775 are co-prime.

Hence, the Greatest Common Factor (GCF) of 828 and 775 is 1.

How Many Factors of 828 are also Factors of 453?

Since, the factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828 and the factors of 453 are 1, 3, 151, 453.
Hence, [1, 3] are the common factors of 828 and 453.

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