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Factors of 480

Factors of 480 are the list of integers that we can split evenly into 480. There are 24 factors of 480 of which 480 itself is the biggest factor and its prime factors are 2, 3, 5 The sum of all factors of 480 is 1512.

  • All Factors of 480: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240 and 480
  • Prime Factors of 480: 2, 3, 5
  • Prime Factorization of 480: 25 × 31 × 51
  • Sum of Factors of 480: 1512
1. What Are the Factors of 480?
2. Factors of 480 by Prime Factorization
3. Factors of 480 in Pairs
4. FAQs on Factors of 480
Factors of 480

What are Factors of 480?

Factors of 480 are pairs of those numbers whose products result in 480. These factors are either prime numbers or composite numbers.

How to Find the Factors of 480?

To find the factors of 480, we will have to find the list of numbers that would divide 480 without leaving any remainder.

  • 480/10 = 48; therefore, 10 is a factor of 480 and 48 is also a factor of 480.
  • 480/160 = 3; therefore, 160 is a factor of 480 and 3 is also a factor of 480.
Similarly we can find other factors. Hence, the factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480.

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Factors of 480 by Prime Factorization

The number 480 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 480. The first step is to divide the number 480 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 480 ÷ 2 = 240
  • 240 ÷ 2 = 120
  • 120 ÷ 2 = 60
  • 60 ÷ 2 = 30
  • 30 ÷ 2 = 15

Further dividing 15 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 15 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 480 can be written as 25 × 31 × 51 where 2, 3, 5 are prime.

 

Factors of 480 in Pairs

Pair factors of 480 are the pairs of numbers that when multiplied give the product 480. The factors of 480 in pairs are:

  • 1 × 480 = (1, 480)
  • 2 × 240 = (2, 240)
  • 3 × 160 = (3, 160)
  • 4 × 120 = (4, 120)
  • 5 × 96 = (5, 96)
  • 6 × 80 = (6, 80)
  • 8 × 60 = (8, 60)
  • 10 × 48 = (10, 48)
  • 12 × 40 = (12, 40)
  • 15 × 32 = (15, 32)
  • 16 × 30 = (16, 30)
  • 20 × 24 = (20, 24)

Negative pair factors of 480 are:

  • -1 × -480 = (-1, -480)
  • -2 × -240 = (-2, -240)
  • -3 × -160 = (-3, -160)
  • -4 × -120 = (-4, -120)
  • -5 × -96 = (-5, -96)
  • -6 × -80 = (-6, -80)
  • -8 × -60 = (-8, -60)
  • -10 × -48 = (-10, -48)
  • -12 × -40 = (-12, -40)
  • -15 × -32 = (-15, -32)
  • -16 × -30 = (-16, -30)
  • -20 × -24 = (-20, -24)

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

Factors of 480 Solved Examples

  1. Example 1: How many factors are there for 480?

    Solution:

    The factors of 480 are too many, therefore if we can find the prime factorization of 480, 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 480 = 25 × 31 × 51
    Therefore, the total number of factors are (5 + 1) × (1 + 1) × (1 + 1) = 6 × 2 × 2 = 24

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 480 and 98.

    Solution:

    The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480 and factors of 98 are 1, 2, 7, 14, 49, 98.

    Therefore, the Least Common Multiple of 480 and 98 is 23520 and Greatest Common Divisor (GCD) of 480 and 98 is 2.

  3. Example 3: Find if 4, 6, 12, 15, 20, 24, 152 and 480 are factors of 480.

    Solution:

    When we divide 480 by 152 it leaves a remainder. Therefore, the number 152 is not a factor of 480. All numbers except 152 are factors of 480.

  4. Example 4: Find the product of all the prime factors of 480.

    Solution:

    Since, the prime factors of 480 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 480

What are the Factors of 480?

The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -80, -96, -120, -160, -240, -480.

What is the Sum of all Factors of 480?

Sum of all factors of 480 = (25 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 1512

What Numbers are the Prime Factors of 480?

The prime factors of 480 are 2, 3, 5.

What is the Greatest Common Factor of 480 and 37?

The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480 and the factors of 37 are 1, 37. 480 and 37 have only one common factor which is 1. This implies that 480 and 37 are co-prime.

Hence, the Greatest Common Factor (GCF) of 480 and 37 is 1.

How Many Factors of 480 are also common to the Factors of 306?

Since, the factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480 and the factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306.
Hence, [1, 2, 3, 6] are the common factors of 480 and 306.

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