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Factors of 2430

Factors of 2430 are numbers that, when multiplied in pairs give the product as 2430. There are total 24 factors of 2430, of which 2, 3, 5 are its prime factors. The sum of all factors of 2430 is 6552.

  • All Factors of 2430: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215 and 2430
  • Prime Factors of 2430: 2, 3, 5
  • Prime Factorization of 2430: 21 × 35 × 51
  • Sum of Factors of 2430: 6552
1. What Are the Factors of 2430?
2. Factors of 2430 by Prime Factorization
3. Factors of 2430 in Pairs
4. FAQs on Factors of 2430
Factors of 2430

What are Factors of 2430?

Factors of 2430 are pairs of those numbers whose products result in 2430. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2430?

To find the factors of 2430, we will have to find the list of numbers that would divide 2430 without leaving any remainder.

  • 2430/3 = 810; therefore, 3 is a factor of 2430 and 810 is also a factor of 2430.
  • 2430/54 = 45; therefore, 54 is a factor of 2430 and 45 is also a factor of 2430.
Similarly we can find other factors. Hence, the factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430.

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Factors of 2430 by Prime Factorization

The number 2430 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2430. The first step is to divide the number 2430 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2430 ÷ 2 = 1215

Further dividing 1215 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1215 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 2430 can be written as 21 × 35 × 51 where 2, 3, 5 are prime.

 

Factors of 2430 in Pairs

Pair factors of 2430 are the pairs of numbers that when multiplied give the product 2430. The factors of 2430 in pairs are:

  • 1 × 2430 = (1, 2430)
  • 2 × 1215 = (2, 1215)
  • 3 × 810 = (3, 810)
  • 5 × 486 = (5, 486)
  • 6 × 405 = (6, 405)
  • 9 × 270 = (9, 270)
  • 10 × 243 = (10, 243)
  • 15 × 162 = (15, 162)
  • 18 × 135 = (18, 135)
  • 27 × 90 = (27, 90)
  • 30 × 81 = (30, 81)
  • 45 × 54 = (45, 54)

Negative pair factors of 2430 are:

  • -1 × -2430 = (-1, -2430)
  • -2 × -1215 = (-2, -1215)
  • -3 × -810 = (-3, -810)
  • -5 × -486 = (-5, -486)
  • -6 × -405 = (-6, -405)
  • -9 × -270 = (-9, -270)
  • -10 × -243 = (-10, -243)
  • -15 × -162 = (-15, -162)
  • -18 × -135 = (-18, -135)
  • -27 × -90 = (-27, -90)
  • -30 × -81 = (-30, -81)
  • -45 × -54 = (-45, -54)

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

Factors of 2430 Solved Examples

  1. Example 1: How many factors are there for 2430?

    Solution:

    The factors of 2430 are too many, therefore if we can find the prime factorization of 2430, 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 2430 = 21 × 35 × 51
    Therefore, the total number of factors are (1 + 1) × (5 + 1) × (1 + 1) = 2 × 6 × 2 = 24

  2. Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 2430 and 942.

    Solution:

    The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430 and factors of 942 are 1, 2, 3, 6, 157, 314, 471, 942.

    Therefore, the Least Common Multiple of 2430 and 942 is 381510 and Highest Common Factor (HCF) of 2430 and 942 is 6.

  3. Example 3: Find if 1, 5, 6, 10, 15, 30, 753 and 2430 are factors of 2430.

    Solution:

    When we divide 2430 by 753 it leaves a remainder. Therefore, the number 753 is not a factor of 2430. All numbers except 753 are factors of 2430.

  4. Example 4: Find the product of all the prime factors of 2430.

    Solution:

    Since, the prime factors of 2430 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 2430

What are the Factors of 2430?

The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430 and its negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -81, -90, -135, -162, -243, -270, -405, -486, -810, -1215, -2430.

What is the Sum of Factors of 2430?

Sum of all factors of 2430 = (21 + 1 - 1)/(2 - 1) × (35 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 6552

What are the Prime Factors of 2430?

The prime factors of 2430 are 2, 3, 5.

What is the Greatest Common Factor of 2430 and 1303?

The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430 and the factors of 1303 are 1, 1303. 2430 and 1303 have only one common factor which is 1. This implies that 2430 and 1303 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2430 and 1303 is 1.

How Many Factors of 2430 are also Factors of 237?

Since, the factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, 2430 and the factors of 237 are 1, 3, 79, 237.
Hence, [1, 3] are the common factors of 2430 and 237.

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