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Factors of 4000

Factors of 4000 are integers that can be divided evenly into 4000. There are overall 24 factors of 4000 among which 4000 is the biggest factor and 2, 5 are its prime factors. The sum of all factors of 4000 is 9828.

All Factors of 4000: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000 and 4000
Prime Factors of 4000: 2, 5
Prime Factorization of 4000: 2⁵ × 5³
Sum of Factors of 4000: 9828

1.	What Are the Factors of 4000?
2.	Factors of 4000 by Prime Factorization
3.	Factors of 4000 in Pairs
4.	FAQs on Factors of 4000

What are Factors of 4000?

Factors of 4000 are pairs of those numbers whose products result in 4000. These factors are either prime numbers or composite numbers.

How to Find the Factors of 4000?

To find the factors of 4000, we will have to find the list of numbers that would divide 4000 without leaving any remainder.

4000/1000 = 4; therefore, 1000 is a factor of 4000 and 4 is also a factor of 4000.
4000/50 = 80; therefore, 50 is a factor of 4000 and 80 is also a factor of 4000.

Similarly we can find other factors. Hence, the factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000.

☛ Also Check:

Factors of 25 - The factors of 25 are 1, 5, 25
Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81
Factors of 11 - The factors of 11 are 1, 11
Factors of 12 - The factors of 12 are 1, 2, 3, 4, 6, 12

Factors of 4000 by Prime Factorization

The number 4000 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 4000. The first step is to divide the number 4000 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

4000 ÷ 2 = 2000
2000 ÷ 2 = 1000
1000 ÷ 2 = 500
500 ÷ 2 = 250
250 ÷ 2 = 125

Further dividing 125 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 125 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 4000 can be written as 2⁵ × 5³ where 2, 5 are prime.

Factors of 4000 in Pairs

Pair factors of 4000 are the pairs of numbers that when multiplied give the product 4000. The factors of 4000 in pairs are:

1 × 4000 = (1, 4000)
2 × 2000 = (2, 2000)
4 × 1000 = (4, 1000)
5 × 800 = (5, 800)
8 × 500 = (8, 500)
10 × 400 = (10, 400)
16 × 250 = (16, 250)
20 × 200 = (20, 200)
25 × 160 = (25, 160)
32 × 125 = (32, 125)
40 × 100 = (40, 100)
50 × 80 = (50, 80)

Negative pair factors of 4000 are:

-1 × -4000 = (-1, -4000)
-2 × -2000 = (-2, -2000)
-4 × -1000 = (-4, -1000)
-5 × -800 = (-5, -800)
-8 × -500 = (-8, -500)
-10 × -400 = (-10, -400)
-16 × -250 = (-16, -250)
-20 × -200 = (-20, -200)
-25 × -160 = (-25, -160)
-32 × -125 = (-32, -125)
-40 × -100 = (-40, -100)
-50 × -80 = (-50, -80)

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

Factors of 4000 Solved Examples

Example 1: How many factors are there for 4000?

Solution:

The factors of 4000 are too many, therefore if we can find the prime factorization of 4000, 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 4000 = 2⁵ × 5³
Therefore, the total number of factors are (5 + 1) × (3 + 1) = 6 × 4 = 24
Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 4000 and 2732.

Solution:

The factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 and factors of 2732 are 1, 2, 4, 683, 1366, 2732.

Therefore, the Least Common Multiple of 4000 and 2732 is 2732000 and Greatest Common Factor (GCF) of 4000 and 2732 is 4.
Example 3: Find if 1, 2, 10, 20, 100, 1975, 2000 and 4000 are factors of 4000.

Solution:

When we divide 4000 by 1975 it leaves a remainder. Therefore, the number 1975 is not a factor of 4000. All numbers except 1975 are factors of 4000.
Example 4: Find the product of all the prime factors of 4000.

Solution:

Since, the prime factors of 4000 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 4000

What are the Factors of 4000?

The factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 and its negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -125, -160, -200, -250, -400, -500, -800, -1000, -2000, -4000.

What is the Sum of all Factors of 4000?

Sum of all factors of 4000 = (2^{5 + 1} - 1)/(2 - 1) × (5^{3 + 1} - 1)/(5 - 1) = 9828

What are Pair Factors of 4000?

The pair factors of 4000 are (1, 4000), (2, 2000), (4, 1000), (5, 800), (8, 500), (10, 400), (16, 250), (20, 200), (25, 160), (32, 125), (40, 100), (50, 80).

What is the Greatest Common Factor of 4000 and 2418?

The factors of 4000 and 2418 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 and 1, 2, 3, 6, 13, 26, 31, 39, 62, 78, 93, 186, 403, 806, 1209, 2418 respectively.

Common factors of 4000 and 2418 are [1, 2].

Hence, the Greatest Common Factor (GCF) of 4000 and 2418 is 2.

How Many Factors of 4000 are also Factors of 3479?

Since, the factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 and factors of 3479 are 1, 7, 49, 71, 497, 3479. Hence, 4000 and 3479 have only one common factor which is 1. Therefore, 4000 and 3479 are co-prime.

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