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Factors of 390

Factors of 390 are the list of integers that we can split evenly into 390. There are 16 factors of 390, of which the following are its prime factors 2, 3, 5, 13. The Prime Factorization of 390 is 21 × 31 × 51 × 131.

  • All Factors of 390: 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195 and 390
  • Prime Factors of 390: 2, 3, 5, 13
  • Prime Factorization of 390: 21 × 31 × 51 × 131
  • Sum of Factors of 390: 1008
1. What Are the Factors of 390?
2. Factors of 390 by Prime Factorization
3. Factors of 390 in Pairs
4. FAQs on Factors of 390
Factors of 390

What are Factors of 390?

Factors of 390 are pairs of those numbers whose products result in 390. These factors are either prime numbers or composite numbers.

How to Find the Factors of 390?

To find the factors of 390, we will have to find the list of numbers that would divide 390 without leaving any remainder.

  • 390/1 = 390; therefore, 1 is a factor of 390.
  • 390/15 = 26; therefore, 15 is a factor of 390.
Similarly we can find other factors. Hence, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390.

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Factors of 390 by Prime Factorization

The number 390 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 390. The first step is to divide the number 390 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 390 ÷ 2 = 195

Further dividing 195 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 195 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 390 can be written as 21 × 31 × 51 × 131 where 2, 3, 5, 13 are prime.

 

Factors of 390 in Pairs

Pair factors of 390 are the pairs of numbers that when multiplied give the product 390. The factors of 390 in pairs are:

  • 1 × 390 = (1, 390)
  • 2 × 195 = (2, 195)
  • 3 × 130 = (3, 130)
  • 5 × 78 = (5, 78)
  • 6 × 65 = (6, 65)
  • 10 × 39 = (10, 39)
  • 13 × 30 = (13, 30)
  • 15 × 26 = (15, 26)

Negative pair factors of 390 are:

  • -1 × -390 = (-1, -390)
  • -2 × -195 = (-2, -195)
  • -3 × -130 = (-3, -130)
  • -5 × -78 = (-5, -78)
  • -6 × -65 = (-6, -65)
  • -10 × -39 = (-10, -39)
  • -13 × -30 = (-13, -30)
  • -15 × -26 = (-15, -26)

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

Factors of 390 Solved Examples

  1. Example 1: How many factors are there for 390?

    Solution:

    The factors of 390 are too many, therefore if we can find the prime factorization of 390, 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 390 = 21 × 31 × 51 × 131
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 390 and 183.

    Solution:

    The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390 and factors of 183 are 1, 3, 61, 183.

    Therefore, the Least Common Multiple (LCM) of 390 and 183 is 23790 and Greatest Common Divisor (GCD) of 390 and 183 is 3.

  3. Example 3: Find if 6, 10, 30, 39, 78, 130, 349 and 390 are factors of 390.

    Solution:

    When we divide 390 by 349 it leaves a remainder. Therefore, the number 349 is not a factor of 390. All numbers except 349 are factors of 390.

  4. Example 4: Find the product of all the prime factors of 390.

    Solution:

    Since, the prime factors of 390 are 2, 3, 5, 13. Therefore, the product of prime factors = 2 × 3 × 5 × 13 = 390.

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FAQs on Factors of 390

What are the Factors of 390?

The factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390 and its negative factors are -1, -2, -3, -5, -6, -10, -13, -15, -26, -30, -39, -65, -78, -130, -195, -390.

What is the Sum of the Factors of 390?

Sum of all factors of 390 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 1008

What numbers are the Pair Factors of 390?

The pair factors of 390 are (1, 390), (2, 195), (3, 130), (5, 78), (6, 65), (10, 39), (13, 30), (15, 26).

What is the Greatest Common Factor of 390 and 141?

The factors of 390 and 141 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390 and 1, 3, 47, 141 respectively.

Common factors of 390 and 141 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 390 and 141 is 3.

How Many Factors of 390 are also Factors of 169?

Since, the factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390 and the factors of 169 are 1, 13, 169.
Hence, [1, 13] are the common factors of 390 and 169.

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