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Factors of 486

Factors of 486 are the list of integers that can be evenly divided into 486. There are 12 factors of 486 of which 486 itself is the biggest factor and its prime factors are 2, 3 The Prime Factorization of 486 is 21 × 35.

  • All Factors of 486: 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 and 486
  • Prime Factors of 486: 2, 3
  • Prime Factorization of 486: 21 × 35
  • Sum of Factors of 486: 1092
1. What Are the Factors of 486?
2. Factors of 486 by Prime Factorization
3. Factors of 486 in Pairs
4. FAQs on Factors of 486
Factors of 486

What are Factors of 486?

Factors of 486 are pairs of those numbers whose products result in 486. These factors are either prime numbers or composite numbers.

How to Find the Factors of 486?

To find the factors of 486, we will have to find the list of numbers that would divide 486 without leaving any remainder.

  • 486/243 = 2; therefore, 243 is a factor of 486 and 2 is also a factor of 486.
  • 486/162 = 3; therefore, 162 is a factor of 486 and 3 is also a factor of 486.
Similarly we can find other factors. Hence, the factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486.

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Factors of 486 by Prime Factorization

The number 486 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 486. The first step is to divide the number 486 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 486 ÷ 2 = 243

Further dividing 243 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 243 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 486 can be written as 21 × 35 where 2, 3 are prime.

 

Factors of 486 in Pairs

Pair factors of 486 are the pairs of numbers that when multiplied give the product 486. The factors of 486 in pairs are:

  • 1 × 486 = (1, 486)
  • 2 × 243 = (2, 243)
  • 3 × 162 = (3, 162)
  • 6 × 81 = (6, 81)
  • 9 × 54 = (9, 54)
  • 18 × 27 = (18, 27)

Negative pair factors of 486 are:

  • -1 × -486 = (-1, -486)
  • -2 × -243 = (-2, -243)
  • -3 × -162 = (-3, -162)
  • -6 × -81 = (-6, -81)
  • -9 × -54 = (-9, -54)
  • -18 × -27 = (-18, -27)

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

Factors of 486 Solved Examples

  1. Example 1: How many factors are there for 486?

    Solution:

    The factors of 486 are too many, therefore if we can find the prime factorization of 486, 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 486 = 21 × 35
    Therefore, the total number of factors are (1 + 1) × (5 + 1) = 2 × 6 = 12

  2. Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 486 and 94.

    Solution:

    The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486 and factors of 94 are 1, 2, 47, 94.

    Therefore, the Least Common Multiple of 486 and 94 is 22842 and Greatest Common Factor (GCF) of 486 and 94 is 2.

  3. Example 3: Find if 1, 3, 9, 162, 243, 401 and 486 are factors of 486.

    Solution:

    When we divide 486 by 401 it leaves a remainder. Therefore, the number 401 is not a factor of 486. All numbers except 401 are factors of 486.

  4. Example 4: Find the product of all the prime factors of 486.

    Solution:

    Since, the prime factors of 486 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.

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FAQs on Factors of 486

What are the Factors of 486?

The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486 and its negative factors are -1, -2, -3, -6, -9, -18, -27, -54, -81, -162, -243, -486.

What is the Sum of the Factors of 486?

Sum of all factors of 486 = (21 + 1 - 1)/(2 - 1) × (35 + 1 - 1)/(3 - 1) = 1092

What Numbers are the Prime Factors of 486?

The prime factors of 486 are 2, 3.

What is the Greatest Common Factor of 486 and 317?

The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486 and the factors of 317 are 1, 317. 486 and 317 have only one common factor which is 1. This implies that 486 and 317 are co-prime.

Hence, the Greatest Common Factor (GCF) of 486 and 317 is 1.

How Many Factors of 241 are also common to the Factors of 486?

Since, the factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486 and factors of 241 are 1, 241. Hence, 486 and 241 have only one common factor which is 1. Therefore, 486 and 241 are co-prime.

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