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Factors of 804

Factors of 804 are numbers that, when multiplied in pairs give the product as 804. There are overall 12 factors of 804 among which 804 is the biggest factor and its prime factors are 2, 3, 67. The Prime Factorization of 804 is 22 × 31 × 671.

  • All Factors of 804: 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402 and 804
  • Prime Factors of 804: 2, 3, 67
  • Prime Factorization of 804: 22 × 31 × 671
  • Sum of Factors of 804: 1904
1. What Are the Factors of 804?
2. Factors of 804 by Prime Factorization
3. Factors of 804 in Pairs
4. FAQs on Factors of 804
Factors of 804

What are Factors of 804?

Factors of 804 are pairs of those numbers whose products result in 804. These factors are either prime numbers or composite numbers.

How to Find the Factors of 804?

To find the factors of 804, we will have to find the list of numbers that would divide 804 without leaving any remainder.

  • 804/804 = 1; therefore, 804 is a factor of 804.
  • 804/6 = 134; therefore, 6 is a factor of 804.
Similarly we can find other factors. Hence, the factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804.

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Factors of 804 by Prime Factorization

The number 804 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 804. The first step is to divide the number 804 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 804 ÷ 2 = 402
  • 402 ÷ 2 = 201

Further dividing 201 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 201 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 804 can be written as 22 × 31 × 671 where 2, 3, 67 are prime.

 

Factors of 804 in Pairs

Pair factors of 804 are the pairs of numbers that when multiplied give the product 804. The factors of 804 in pairs are:

  • 1 × 804 = (1, 804)
  • 2 × 402 = (2, 402)
  • 3 × 268 = (3, 268)
  • 4 × 201 = (4, 201)
  • 6 × 134 = (6, 134)
  • 12 × 67 = (12, 67)

Negative pair factors of 804 are:

  • -1 × -804 = (-1, -804)
  • -2 × -402 = (-2, -402)
  • -3 × -268 = (-3, -268)
  • -4 × -201 = (-4, -201)
  • -6 × -134 = (-6, -134)
  • -12 × -67 = (-12, -67)

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

Factors of 804 Solved Examples

  1. Example 1: How many factors are there for 804?

    Solution:

    The factors of 804 are too many, therefore if we can find the prime factorization of 804, 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 804 = 22 × 31 × 671
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 804 and 106.

    Solution:

    The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804 and factors of 106 are 1, 2, 53, 106.

    Therefore, the Lowest Common Multiple (LCM) of 804 and 106 is 42612 and Highest Common Factor (HCF) of 804 and 106 is 2.

  3. Example 3: Find if 4, 6, 12, 134, 201, 227 and 268 are factors of 804.

    Solution:

    When we divide 804 by 227 it leaves a remainder. Therefore, the number 227 is not a factor of 804. All numbers except 227 are factors of 804.

  4. Example 4: Find the product of all the prime factors of 804.

    Solution:

    Since, the prime factors of 804 are 2, 3, 67. Therefore, the product of prime factors = 2 × 3 × 67 = 402.

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FAQs on Factors of 804

What are the Factors of 804?

The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804 and its negative factors are -1, -2, -3, -4, -6, -12, -67, -134, -201, -268, -402, -804.

What is the Sum of all the Factors of 804?

Sum of all factors of 804 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (671 + 1 - 1)/(67 - 1) = 1904

What numbers are the Pair Factors of 804?

The pair factors of 804 are (1, 804), (2, 402), (3, 268), (4, 201), (6, 134), (12, 67).

What is the Greatest Common Factor of 804 and 134?

The factors of 804 and 134 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804 and 1, 2, 67, 134 respectively.

Common factors of 804 and 134 are [1, 2, 67, 134].

Hence, the Greatest Common Factor (GCF) of 804 and 134 is 134.

How Many Factors of 231 are also common to the Factors of 804?

Since, the factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804 and the factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231.
Hence, [1, 3] are the common factors of 804 and 231.

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