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Factors of 2000

Factors of 2000 are integers that can be divided evenly into 2000. There are overall 20 factors of 2000 among which 2000 is the biggest factor and 2, 5 are its prime factors. The sum of all factors of 2000 is 4836.

All Factors of 2000: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000 and 2000
Prime Factors of 2000: 2, 5
Prime Factorization of 2000: 2⁴ × 5³
Sum of Factors of 2000: 4836

1.	What Are the Factors of 2000?
2.	Factors of 2000 by Prime Factorization
3.	Factors of 2000 in Pairs
4.	FAQs on Factors of 2000

What are Factors of 2000?

Factors of 2000 are pairs of those numbers whose products result in 2000. These factors are either prime numbers or composite numbers.

How to Find the Factors of 2000?

To find the factors of 2000, we will have to find the list of numbers that would divide 2000 without leaving any remainder.

2000/200 = 10; therefore, 200 is a factor of 2000 and 10 is also a factor of 2000.
2000/250 = 8; therefore, 250 is a factor of 2000 and 8 is also a factor of 2000.

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

☛ Also Check:

Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 55 - The factors of 55 are 1, 5, 11, 55
Factors of 10 - The factors of 10 are 1, 2, 5, 10

Factors of 2000 by Prime Factorization

The number 2000 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 2000. The first step is to divide the number 2000 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

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 2000 can be written as 2⁴ × 5³ where 2, 5 are prime.

Factors of 2000 in Pairs

Pair factors of 2000 are the pairs of numbers that when multiplied give the product 2000. The factors of 2000 in pairs are:

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

Negative pair factors of 2000 are:

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

Example 1: How many factors are there for 2000?

Solution:

The factors of 2000 are too many, therefore if we can find the prime factorization of 2000, 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 2000 = 2⁴ × 5³
Therefore, the total number of factors are (4 + 1) × (3 + 1) = 5 × 4 = 20
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 2000 and 356.

Solution:

The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 and factors of 356 are 1, 2, 4, 89, 178, 356.

Therefore, the Lowest Common Multiple (LCM) of 2000 and 356 is 178000 and Greatest Common Divisor (GCD) of 2000 and 356 is 4.
Example 3: Find if 2, 10, 20, 40, 100, 250, 400 and 1513 are factors of 2000.

Solution:

When we divide 2000 by 1513 it leaves a remainder. Therefore, the number 1513 is not a factor of 2000. All numbers except 1513 are factors of 2000.
Example 4: Find the product of all the prime factors of 2000.

Solution:

Since, the prime factors of 2000 are 2, 5. Therefore, the product of prime factors = 2 × 5 = 10.

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FAQs on Factors of 2000

What are the Factors of 2000?

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

What is the Sum of Factors of 2000?

Sum of all factors of 2000 = (2^{4 + 1} - 1)/(2 - 1) × (5^{3 + 1} - 1)/(5 - 1) = 4836

What Numbers are the Prime Factors of 2000?

The prime factors of 2000 are 2, 5.

What is the Greatest Common Factor of 2000 and 157?

The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 and the factors of 157 are 1, 157. 2000 and 157 have only one common factor which is 1. This implies that 2000 and 157 are co-prime.

Hence, the Greatest Common Factor (GCF) of 2000 and 157 is 1.

How Many Factors of 837 are also common to the Factors of 2000?

Since, the factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000 and factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837. Hence, 2000 and 837 have only one common factor which is 1. Therefore, 2000 and 837 are co-prime.

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