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Factors of 5000

Factors of 5000 are the list of integers that can be evenly divided into 5000. There are 20 factors of 5000, of which the following are its prime factors 2, 5. The Prime Factorization of 5000 is 2³ × 5⁴.

All Factors of 5000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500 and 5000
Prime Factors of 5000: 2, 5
Prime Factorization of 5000: 2³ × 5⁴
Sum of Factors of 5000: 11715

1.	What Are the Factors of 5000?
2.	Factors of 5000 by Prime Factorization
3.	Factors of 5000 in Pairs
4.	FAQs on Factors of 5000

What are Factors of 5000?

Factors of 5000 are pairs of those numbers whose products result in 5000. These factors are either prime numbers or composite numbers.

How to Find the Factors of 5000?

To find the factors of 5000, we will have to find the list of numbers that would divide 5000 without leaving any remainder.

5000/500 = 10; therefore, 500 is a factor of 5000 and 10 is also a factor of 5000.
5000/2 = 2500; therefore, 2 is a factor of 5000 and 2500 is also a factor of 5000.

Similarly we can find other factors. Hence, the factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000.

☛ Also Check:

Factors of 21 - The factors of 21 are 1, 3, 7, 21
Factors of 38 - The factors of 38 are 1, 2, 19, 38
Factors of 6 - The factors of 6 are 1, 2, 3, 6
Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
Factors of 37 - The factors of 37 are 1, 37

Factors of 5000 by Prime Factorization

The number 5000 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 5000. The first step is to divide the number 5000 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

5000 ÷ 2 = 2500
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 5000 can be written as 2³ × 5⁴ where 2, 5 are prime.

Factors of 5000 in Pairs

Pair factors of 5000 are the pairs of numbers that when multiplied give the product 5000. The factors of 5000 in pairs are:

1 × 5000 = (1, 5000)
2 × 2500 = (2, 2500)
4 × 1250 = (4, 1250)
5 × 1000 = (5, 1000)
8 × 625 = (8, 625)
10 × 500 = (10, 500)
20 × 250 = (20, 250)
25 × 200 = (25, 200)
40 × 125 = (40, 125)
50 × 100 = (50, 100)

Negative pair factors of 5000 are:

-1 × -5000 = (-1, -5000)
-2 × -2500 = (-2, -2500)
-4 × -1250 = (-4, -1250)
-5 × -1000 = (-5, -1000)
-8 × -625 = (-8, -625)
-10 × -500 = (-10, -500)
-20 × -250 = (-20, -250)
-25 × -200 = (-25, -200)
-40 × -125 = (-40, -125)
-50 × -100 = (-50, -100)

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

Factors of 5000 Solved Examples

Example 1: How many factors are there for 5000?

Solution:

The factors of 5000 are too many, therefore if we can find the prime factorization of 5000, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z 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 5000 = 2³ × 5⁴
Therefore, the total number of factors are (3 + 1) × (4 + 1) = 4 × 5 = 20
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 5000 and 562.

Solution:

The factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000 and factors of 562 are 1, 2, 281, 562.

Therefore, the Least Common Multiple of 5000 and 562 is 1405000 and Highest Common Factor (HCF) of 5000 and 562 is 2.
Example 3: Find if 4, 5, 8, 10, 40, 100, 625 and 2402 are factors of 5000.

Solution:

When we divide 5000 by 2402 it leaves a remainder. Therefore, the number 2402 is not a factor of 5000. All numbers except 2402 are factors of 5000.
Example 4: Find the product of all the prime factors of 5000.

Solution:

Since, the prime factors of 5000 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 5000

What are the Factors of 5000?

The factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000 and its negative factors are -1, -2, -4, -5, -8, -10, -20, -25, -40, -50, -100, -125, -200, -250, -500, -625, -1000, -1250, -2500, -5000.

What is the Sum of all the Factors of 5000?

Sum of all factors of 5000 = (2^{3 + 1} - 1)/(2 - 1) × (5^{4 + 1} - 1)/(5 - 1) = 11715

What numbers are the Pair Factors of 5000?

The pair factors of 5000 are (1, 5000), (2, 2500), (4, 1250), (5, 1000), (8, 625), (10, 500), (20, 250), (25, 200), (40, 125), (50, 100).

What is the Greatest Common Factor of 5000 and 3980?

The factors of 5000 and 3980 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000 and 1, 2, 4, 5, 10, 20, 199, 398, 796, 995, 1990, 3980 respectively.

Common factors of 5000 and 3980 are [1, 2, 4, 5, 10, 20].

Hence, the Greatest Common Factor of 5000 and 3980 is 20.

How Many Factors of 5000 are also common to the Factors of 2553?

Since, the factors of 5000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 625, 1000, 1250, 2500, 5000 and factors of 2553 are 1, 3, 23, 37, 69, 111, 851, 2553. Hence, 5000 and 2553 have only one common factor which is 1. Therefore, 5000 and 2553 are co-prime.

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