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Factors of 585

Factors of 585 are numbers that, when multiplied in pairs give the product as 585. There are 12 factors of 585, of which the following are its prime factors 3, 5, 13. The sum of all factors of 585 is 1092.

  • All Factors of 585: 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195 and 585
  • Prime Factors of 585: 3, 5, 13
  • Prime Factorization of 585: 32 × 51 × 131
  • Sum of Factors of 585: 1092
1. What Are the Factors of 585?
2. Factors of 585 by Prime Factorization
3. Factors of 585 in Pairs
4. FAQs on Factors of 585
Factors of 585

What are Factors of 585?

Factors of 585 are pairs of those numbers whose products result in 585. These factors are either prime numbers or composite numbers.

How to Find the Factors of 585?

To find the factors of 585, we will have to find the list of numbers that would divide 585 without leaving any remainder.

  • 585/39 = 15; therefore, 39 is a factor of 585 and 15 is also a factor of 585.
  • 585/117 = 5; therefore, 117 is a factor of 585 and 5 is also a factor of 585.
Similarly we can find other factors. Hence, the factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585.

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Factors of 585 by Prime Factorization

The number 585 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 585. The first step is to divide the number 585 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
  • 585 ÷ 3 = 195
  • 195 ÷ 3 = 65

Further dividing 65 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 65 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 585 can be written as 32 × 51 × 131 where 3, 5, 13 are prime.

 

Factors of 585 in Pairs

Pair factors of 585 are the pairs of numbers that when multiplied give the product 585. The factors of 585 in pairs are:

  • 1 × 585 = (1, 585)
  • 3 × 195 = (3, 195)
  • 5 × 117 = (5, 117)
  • 9 × 65 = (9, 65)
  • 13 × 45 = (13, 45)
  • 15 × 39 = (15, 39)

Negative pair factors of 585 are:

  • -1 × -585 = (-1, -585)
  • -3 × -195 = (-3, -195)
  • -5 × -117 = (-5, -117)
  • -9 × -65 = (-9, -65)
  • -13 × -45 = (-13, -45)
  • -15 × -39 = (-15, -39)

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

Factors of 585 Solved Examples

  1. Example 1: How many factors are there for 585?

    Solution:

    The factors of 585 are too many, therefore if we can find the prime factorization of 585, 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 585 = 32 × 51 × 131
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 585 and 214.

    Solution:

    The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585 and factors of 214 are 1, 2, 107, 214.

    Therefore, the Least Common Multiple (LCM) of 585 and 214 is 125190 and Greatest Common Divisor (GCD) of 585 and 214 is 1.

  3. Example 3: Find if 9, 37, 39, 45, 117, 195 and 585 are factors of 585.

    Solution:

    When we divide 585 by 37 it leaves a remainder. Therefore, the number 37 is not a factor of 585. All numbers except 37 are factors of 585.

  4. Example 4: Find the product of all the prime factors of 585.

    Solution:

    Since, the prime factors of 585 are 3, 5, 13. Therefore, the product of prime factors = 3 × 5 × 13 = 195.

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FAQs on Factors of 585

What are the Factors of 585?

The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585 and its negative factors are -1, -3, -5, -9, -13, -15, -39, -45, -65, -117, -195, -585.

What is the Sum of Factors of 585?

Sum of all factors of 585 = (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 1092

What numbers are the Pair Factors of 585?

The pair factors of 585 are (1, 585), (3, 195), (5, 117), (9, 65), (13, 45), (15, 39).

What is the Greatest Common Factor of 585 and 527?

The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585 and the factors of 527 are 1, 17, 31, 527. 585 and 527 have only one common factor which is 1. This implies that 585 and 527 are co-prime.

Hence, the Greatest Common Factor (GCF) of 585 and 527 is 1.

How Many Factors of 585 are also Factors of 321?

Since, the factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585 and the factors of 321 are 1, 3, 107, 321.
Hence, [1, 3] are the common factors of 585 and 321.

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