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Factors of 2500

Factors of 2500 are the list of integers that we can split evenly into 2500. There are 15 factors of 2500 of which 2500 itself is the biggest factor and its prime factors are 2, 5 The Prime Factorization of 2500 is 22 × 54.

  • All Factors of 2500: 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250 and 2500
  • Prime Factors of 2500: 2, 5
  • Prime Factorization of 2500: 22 × 54
  • Sum of Factors of 2500: 5467
1. What Are the Factors of 2500?
2. Factors of 2500 by Prime Factorization
3. Factors of 2500 in Pairs
4. FAQs on Factors of 2500
Factors of 2500

What are Factors of 2500?

Factors of 2500 are pairs of those numbers whose products result in 2500. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2500?

To find the factors of 2500, we will have to find the list of numbers that would divide 2500 without leaving any remainder.

  • 2500/625 = 4; therefore, 625 is a factor of 2500 and 4 is also a factor of 2500.
  • 2500/2 = 1250; therefore, 2 is a factor of 2500 and 1250 is also a factor of 2500.
Similarly we can find other factors. Hence, the factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500.

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Factors of 2500 by Prime Factorization

The number 2500 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2500. The first step is to divide the number 2500 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 2500 ÷ 2 = 1250
  • 1250 ÷ 2 = 625

Further dividing 625 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 625 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 2500 can be written as 22 × 54 where 2, 5 are prime.

 

Factors of 2500 in Pairs

Pair factors of 2500 are the pairs of numbers that when multiplied give the product 2500. The factors of 2500 in pairs are:

  • 1 × 2500 = (1, 2500)
  • 2 × 1250 = (2, 1250)
  • 4 × 625 = (4, 625)
  • 5 × 500 = (5, 500)
  • 10 × 250 = (10, 250)
  • 20 × 125 = (20, 125)
  • 25 × 100 = (25, 100)
  • 50 × 50 = (50, 50)

Negative pair factors of 2500 are:

  • -1 × -2500 = (-1, -2500)
  • -2 × -1250 = (-2, -1250)
  • -4 × -625 = (-4, -625)
  • -5 × -500 = (-5, -500)
  • -10 × -250 = (-10, -250)
  • -20 × -125 = (-20, -125)
  • -25 × -100 = (-25, -100)
  • -50 × -50 = (-50, -50)

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

Factors of 2500 Solved Examples

  1. Example 1: How many factors are there for 2500?

    Solution:

    The factors of 2500 are too many, therefore if we can find the prime factorization of 2500, 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 2500 = 22 × 54
    Therefore, the total number of factors are (2 + 1) × (4 + 1) = 3 × 5 = 15

  2. Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 2500 and 1042.

    Solution:

    The factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500 and factors of 1042 are 1, 2, 521, 1042.

    Therefore, the Lowest Common Multiple (LCM) of 2500 and 1042 is 1302500 and Highest Common Factor (HCF) of 2500 and 1042 is 2.

  3. Example 3: Find if 1, 2, 10, 20, 50, 250, 1208 and 1250 are factors of 2500.

    Solution:

    When we divide 2500 by 1208 it leaves a remainder. Therefore, the number 1208 is not a factor of 2500. All numbers except 1208 are factors of 2500.

  4. Example 4: Find the product of all the prime factors of 2500.

    Solution:

    Since, the prime factors of 2500 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 2500

What are the Factors of 2500?

The factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500 and its negative factors are -1, -2, -4, -5, -10, -20, -25, -50, -100, -125, -250, -500, -625, -1250, -2500.

What is the Sum of the Factors of 2500?

Sum of all factors of 2500 = (22 + 1 - 1)/(2 - 1) × (54 + 1 - 1)/(5 - 1) = 5467

What are Pair Factors of 2500?

The pair factors of 2500 are (1, 2500), (2, 1250), (4, 625), (5, 500), (10, 250), (20, 125), (25, 100), (50, 50).

What is the Greatest Common Factor of 2500 and 2489?

The factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500 and the factors of 2489 are 1, 19, 131, 2489. 2500 and 2489 have only one common factor which is 1. This implies that 2500 and 2489 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2500 and 2489 is 1.

How Many Factors of 2500 are also Factors of 382?

Since, the factors of 2500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500, 625, 1250, 2500 and the factors of 382 are 1, 2, 191, 382.
Hence, [1, 2] are the common factors of 2500 and 382.

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