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Factors of 588

Factors of 588 are integers that can be divided evenly into 588. There are overall 18 factors of 588, of which 2, 3, 7 are its prime factors. The sum of all factors of 588 is 1596.

  • All Factors of 588: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294 and 588
  • Prime Factors of 588: 2, 3, 7
  • Prime Factorization of 588: 22 × 31 × 72
  • Sum of Factors of 588: 1596
1. What Are the Factors of 588?
2. Factors of 588 by Prime Factorization
3. Factors of 588 in Pairs
4. FAQs on Factors of 588
Factors of 588

What are Factors of 588?

Factors of 588 are pairs of those numbers whose products result in 588. These factors are either prime numbers or composite numbers.

How to Find the Factors of 588?

To find the factors of 588, we will have to find the list of numbers that would divide 588 without leaving any remainder.

  • 588/147 = 4; therefore, 147 is a factor of 588 and 4 is also a factor of 588.
  • 588/7 = 84; therefore, 7 is a factor of 588 and 84 is also a factor of 588.
Similarly we can find other factors. Hence, the factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588.

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Factors of 588 by Prime Factorization

The number 588 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 588. The first step is to divide the number 588 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 588 ÷ 2 = 294
  • 294 ÷ 2 = 147

Further dividing 147 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 147 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 588 can be written as 22 × 31 × 72 where 2, 3, 7 are prime.

 

Factors of 588 in Pairs

Pair factors of 588 are the pairs of numbers that when multiplied give the product 588. The factors of 588 in pairs are:

  • 1 × 588 = (1, 588)
  • 2 × 294 = (2, 294)
  • 3 × 196 = (3, 196)
  • 4 × 147 = (4, 147)
  • 6 × 98 = (6, 98)
  • 7 × 84 = (7, 84)
  • 12 × 49 = (12, 49)
  • 14 × 42 = (14, 42)
  • 21 × 28 = (21, 28)

Negative pair factors of 588 are:

  • -1 × -588 = (-1, -588)
  • -2 × -294 = (-2, -294)
  • -3 × -196 = (-3, -196)
  • -4 × -147 = (-4, -147)
  • -6 × -98 = (-6, -98)
  • -7 × -84 = (-7, -84)
  • -12 × -49 = (-12, -49)
  • -14 × -42 = (-14, -42)
  • -21 × -28 = (-21, -28)

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

Factors of 588 Solved Examples

  1. Example 1: How many factors are there for 588?

    Solution:

    The factors of 588 are too many, therefore if we can find the prime factorization of 588, 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 588 = 22 × 31 × 72
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (2 + 1) = 3 × 2 × 3 = 18

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 588 and 461.

    Solution:

    The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 and factors of 461 are 1, 461.

    Therefore, the Least Common Multiple (LCM) of 588 and 461 is 271068 and Highest Common Factor (HCF) of 588 and 461 is 1.

  3. Example 3: Find if 12, 21, 42, 49, 84, 98, 294 and 499 are factors of 588.

    Solution:

    When we divide 588 by 499 it leaves a remainder. Therefore, the number 499 is not a factor of 588. All numbers except 499 are factors of 588.

  4. Example 4: Find the product of all the prime factors of 588.

    Solution:

    Since, the prime factors of 588 are 2, 3, 7. Therefore, the product of prime factors = 2 × 3 × 7 = 42.

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FAQs on Factors of 588

What are the Factors of 588?

The factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 and its negative factors are -1, -2, -3, -4, -6, -7, -12, -14, -21, -28, -42, -49, -84, -98, -147, -196, -294, -588.

What is the Sum of Factors of 588?

Sum of all factors of 588 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (72 + 1 - 1)/(7 - 1) = 1596

What Numbers are the Prime Factors of 588?

The prime factors of 588 are 2, 3, 7.

What is the Greatest Common Factor of 588 and 460?

The factors of 588 and 460 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 and 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460 respectively.

Common factors of 588 and 460 are [1, 2, 4].

Hence, the Greatest Common Factor of 588 and 460 is 4.

How Many Factors of 588 are also common to the Factors of 546?

Since, the factors of 588 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 49, 84, 98, 147, 196, 294, 588 and the factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546.
Hence, [1, 2, 3, 6, 7, 14, 21, 42] are the common factors of 588 and 546.

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