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Factors of 630

Factors of 630 are the list of integers that we can split evenly into 630. There are 24 factors of 630, of which the following are its prime factors 2, 3, 5, 7. The Prime Factorization of 630 is 21 × 32 × 51 × 71.

  • All Factors of 630: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315 and 630
  • Prime Factors of 630: 2, 3, 5, 7
  • Prime Factorization of 630: 21 × 32 × 51 × 71
  • Sum of Factors of 630: 1872
1. What Are the Factors of 630?
2. Factors of 630 by Prime Factorization
3. Factors of 630 in Pairs
4. FAQs on Factors of 630
Factors of 630

What are Factors of 630?

Factors of 630 are pairs of those numbers whose products result in 630. These factors are either prime numbers or composite numbers.

How to Find the Factors of 630?

To find the factors of 630, we will have to find the list of numbers that would divide 630 without leaving any remainder.

  • 630/210 = 3; therefore, 210 is a factor of 630 and 3 is also a factor of 630.
  • 630/70 = 9; therefore, 70 is a factor of 630 and 9 is also a factor of 630.
Similarly we can find other factors. Hence, the factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630.

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Factors of 630 by Prime Factorization

The number 630 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 630. The first step is to divide the number 630 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 630 ÷ 2 = 315

Further dividing 315 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 315 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 630 can be written as 21 × 32 × 51 × 71 where 2, 3, 5, 7 are prime.

 

Factors of 630 in Pairs

Pair factors of 630 are the pairs of numbers that when multiplied give the product 630. The factors of 630 in pairs are:

  • 1 × 630 = (1, 630)
  • 2 × 315 = (2, 315)
  • 3 × 210 = (3, 210)
  • 5 × 126 = (5, 126)
  • 6 × 105 = (6, 105)
  • 7 × 90 = (7, 90)
  • 9 × 70 = (9, 70)
  • 10 × 63 = (10, 63)
  • 14 × 45 = (14, 45)
  • 15 × 42 = (15, 42)
  • 18 × 35 = (18, 35)
  • 21 × 30 = (21, 30)

Negative pair factors of 630 are:

  • -1 × -630 = (-1, -630)
  • -2 × -315 = (-2, -315)
  • -3 × -210 = (-3, -210)
  • -5 × -126 = (-5, -126)
  • -6 × -105 = (-6, -105)
  • -7 × -90 = (-7, -90)
  • -9 × -70 = (-9, -70)
  • -10 × -63 = (-10, -63)
  • -14 × -45 = (-14, -45)
  • -15 × -42 = (-15, -42)
  • -18 × -35 = (-18, -35)
  • -21 × -30 = (-21, -30)

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

Factors of 630 Solved Examples

  1. Example 1: How many factors are there for 630?

    Solution:

    The factors of 630 are too many, therefore if we can find the prime factorization of 630, 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 630 = 21 × 32 × 51 × 71
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 2 × 3 × 2 × 2 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 630 and 193.

    Solution:

    The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630 and factors of 193 are 1, 193.

    Therefore, the Least Common Multiple (LCM) of 630 and 193 is 121590 and Greatest Common Factor (GCF) of 630 and 193 is 1.

  3. Example 3: Find if 1, 6, 9, 21, 30, 105, 496 and 630 are factors of 630.

    Solution:

    When we divide 630 by 496 it leaves a remainder. Therefore, the number 496 is not a factor of 630. All numbers except 496 are factors of 630.

  4. Example 4: Find the product of all the prime factors of 630.

    Solution:

    Since, the prime factors of 630 are 2, 3, 5, 7. Therefore, the product of prime factors = 2 × 3 × 5 × 7 = 210.

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FAQs on Factors of 630

What are the Factors of 630?

The factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630 and its negative factors are -1, -2, -3, -5, -6, -7, -9, -10, -14, -15, -18, -21, -30, -35, -42, -45, -63, -70, -90, -105, -126, -210, -315, -630.

What is the Sum of all the Factors of 630?

Sum of all factors of 630 = (21 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 1872

What numbers are the Pair Factors of 630?

The pair factors of 630 are (1, 630), (2, 315), (3, 210), (5, 126), (6, 105), (7, 90), (9, 70), (10, 63), (14, 45), (15, 42), (18, 35), (21, 30).

What is the Greatest Common Factor of 630 and 620?

The factors of 630 and 620 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630 and 1, 2, 4, 5, 10, 20, 31, 62, 124, 155, 310, 620 respectively.

Common factors of 630 and 620 are [1, 2, 5, 10].

Hence, the Greatest Common Factor (GCF) of 630 and 620 is 10.

How Many Factors of 630 are also Factors of 526?

Since, the factors of 630 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630 and the factors of 526 are 1, 2, 263, 526.
Hence, [1, 2] are the common factors of 630 and 526.

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