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Factors of 980

Factors of 980 are the list of integers that we can split evenly into 980. There are overall 18 factors of 980, of which 2, 5, 7 are its prime factors. The sum of all factors of 980 is 2394.

  • All Factors of 980: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490 and 980
  • Prime Factors of 980: 2, 5, 7
  • Prime Factorization of 980: 22 × 51 × 72
  • Sum of Factors of 980: 2394
1. What Are the Factors of 980?
2. Factors of 980 by Prime Factorization
3. Factors of 980 in Pairs
4. FAQs on Factors of 980
Factors of 980

What are Factors of 980?

Factors of 980 are pairs of those numbers whose products result in 980. These factors are either prime numbers or composite numbers.

How to Find the Factors of 980?

To find the factors of 980, we will have to find the list of numbers that would divide 980 without leaving any remainder.

  • 980/2 = 490; therefore, 2 is a factor of 980 and 490 is also a factor of 980.
  • 980/5 = 196; therefore, 5 is a factor of 980 and 196 is also a factor of 980.
Similarly we can find other factors. Hence, the factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980.

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Factors of 980 by Prime Factorization

The number 980 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 980. The first step is to divide the number 980 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 980 ÷ 2 = 490
  • 490 ÷ 2 = 245

Further dividing 245 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 245 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 980 can be written as 22 × 51 × 72 where 2, 5, 7 are prime.

 

Factors of 980 in Pairs

Pair factors of 980 are the pairs of numbers that when multiplied give the product 980. The factors of 980 in pairs are:

  • 1 × 980 = (1, 980)
  • 2 × 490 = (2, 490)
  • 4 × 245 = (4, 245)
  • 5 × 196 = (5, 196)
  • 7 × 140 = (7, 140)
  • 10 × 98 = (10, 98)
  • 14 × 70 = (14, 70)
  • 20 × 49 = (20, 49)
  • 28 × 35 = (28, 35)

Negative pair factors of 980 are:

  • -1 × -980 = (-1, -980)
  • -2 × -490 = (-2, -490)
  • -4 × -245 = (-4, -245)
  • -5 × -196 = (-5, -196)
  • -7 × -140 = (-7, -140)
  • -10 × -98 = (-10, -98)
  • -14 × -70 = (-14, -70)
  • -20 × -49 = (-20, -49)
  • -28 × -35 = (-28, -35)

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

Factors of 980 Solved Examples

  1. Example 1: How many factors are there for 980?

    Solution:

    The factors of 980 are too many, therefore if we can find the prime factorization of 980, 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 980 = 22 × 51 × 72
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (2 + 1) = 3 × 2 × 3 = 18

  2. Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 980 and 80.

    Solution:

    The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 and factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.

    Therefore, the Least Common Multiple (LCM) of 980 and 80 is 3920 and Highest Common Factor (HCF) of 980 and 80 is 20.

  3. Example 3: Find if 1, 2, 14, 20, 35, 49, 70 and 253 are factors of 980.

    Solution:

    When we divide 980 by 253 it leaves a remainder. Therefore, the number 253 is not a factor of 980. All numbers except 253 are factors of 980.

  4. Example 4: Find the product of all the prime factors of 980.

    Solution:

    Since, the prime factors of 980 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 980

What are the Factors of 980?

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 and its negative factors are -1, -2, -4, -5, -7, -10, -14, -20, -28, -35, -49, -70, -98, -140, -196, -245, -490, -980.

What is the Sum of the Factors of 980?

Sum of all factors of 980 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (72 + 1 - 1)/(7 - 1) = 2394

What are Pair Factors of 980?

The pair factors of 980 are (1, 980), (2, 490), (4, 245), (5, 196), (7, 140), (10, 98), (14, 70), (20, 49), (28, 35).

What is the Greatest Common Factor of 980 and 271?

The factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 and the factors of 271 are 1, 271. 980 and 271 have only one common factor which is 1. This implies that 980 and 271 are co-prime.

Hence, the Greatest Common Factor (GCF) of 980 and 271 is 1.

What are the Common Factors of 980 and 489?

Since, the factors of 980 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980 and factors of 489 are 1, 3, 163, 489. Hence, 980 and 489 have only one common factor which is 1. Therefore, 980 and 489 are co-prime.

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