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Factors of 560

Factors of 560 are numbers that, when multiplied in pairs give the product as 560. There are 20 factors of 560 of which 560 itself is the biggest factor and its prime factors are 2, 5, 7 The Prime Factorization of 560 is 24 × 51 × 71.

  • All Factors of 560: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280 and 560
  • Prime Factors of 560: 2, 5, 7
  • Prime Factorization of 560: 24 × 51 × 71
  • Sum of Factors of 560: 1488
1. What Are the Factors of 560?
2. Factors of 560 by Prime Factorization
3. Factors of 560 in Pairs
4. FAQs on Factors of 560
Factors of 560

What are Factors of 560?

Factors of 560 are pairs of those numbers whose products result in 560. These factors are either prime numbers or composite numbers.

How to Find the Factors of 560?

To find the factors of 560, we will have to find the list of numbers that would divide 560 without leaving any remainder.

  • 560/20 = 28; therefore, 20 is a factor of 560 and 28 is also a factor of 560.
  • 560/7 = 80; therefore, 7 is a factor of 560 and 80 is also a factor of 560.
Similarly we can find other factors. Hence, the factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560.

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Factors of 560 by Prime Factorization

The number 560 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 560. The first step is to divide the number 560 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 560 ÷ 2 = 280
  • 280 ÷ 2 = 140
  • 140 ÷ 2 = 70
  • 70 ÷ 2 = 35

Further dividing 35 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 35 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 560 can be written as 24 × 51 × 71 where 2, 5, 7 are prime.

 

Factors of 560 in Pairs

Pair factors of 560 are the pairs of numbers that when multiplied give the product 560. The factors of 560 in pairs are:

  • 1 × 560 = (1, 560)
  • 2 × 280 = (2, 280)
  • 4 × 140 = (4, 140)
  • 5 × 112 = (5, 112)
  • 7 × 80 = (7, 80)
  • 8 × 70 = (8, 70)
  • 10 × 56 = (10, 56)
  • 14 × 40 = (14, 40)
  • 16 × 35 = (16, 35)
  • 20 × 28 = (20, 28)

Negative pair factors of 560 are:

  • -1 × -560 = (-1, -560)
  • -2 × -280 = (-2, -280)
  • -4 × -140 = (-4, -140)
  • -5 × -112 = (-5, -112)
  • -7 × -80 = (-7, -80)
  • -8 × -70 = (-8, -70)
  • -10 × -56 = (-10, -56)
  • -14 × -40 = (-14, -40)
  • -16 × -35 = (-16, -35)
  • -20 × -28 = (-20, -28)

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

Factors of 560 Solved Examples

  1. Example 1: How many factors are there for 560?

    Solution:

    The factors of 560 are too many, therefore if we can find the prime factorization of 560, 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 560 = 24 × 51 × 71
    Therefore, the total number of factors are (4 + 1) × (1 + 1) × (1 + 1) = 5 × 2 × 2 = 20

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 560 and 509.

    Solution:

    The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 and factors of 509 are 1, 509.

    Therefore, the LCM of 560 and 509 is 285040 and Greatest Common Divisor (GCD) of 560 and 509 is 1.

  3. Example 3: Find if 1, 4, 8, 10, 28, 70, 143 and 560 are factors of 560.

    Solution:

    When we divide 560 by 143 it leaves a remainder. Therefore, the number 143 is not a factor of 560. All numbers except 143 are factors of 560.

  4. Example 4: Find the product of all the prime factors of 560.

    Solution:

    Since, the prime factors of 560 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 560

What are the Factors of 560?

The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 and its negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -35, -40, -56, -70, -80, -112, -140, -280, -560.

What is the Sum of all Factors of 560?

Sum of all factors of 560 = (24 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) = 1488

What Numbers are the Prime Factors of 560?

The prime factors of 560 are 2, 5, 7.

What is the Greatest Common Factor of 560 and 425?

The factors of 560 and 425 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 and 1, 5, 17, 25, 85, 425 respectively.

Common factors of 560 and 425 are [1, 5].

Hence, the Greatest Common Factor of 560 and 425 is 5.

How Many Factors of 524 are also common to the Factors of 560?

Since, the factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560 and the factors of 524 are 1, 2, 4, 131, 262, 524.
Hence, [1, 2, 4] are the common factors of 560 and 524.

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