284 LearnersLast updated on May 26th, 2025
Factors of 2000
What's your say about the factors of 2000? Factors are essentially numbers that can be multiplied together to give an original number. In other words, finding those perfect pairs that go into making 2000 without leaving remainders.
What are the factors of 2000?
Similarly, as we learned above, factors of 2000 are such numbers that will be multiplied to get 2000. There are both positive and negative factors of numbers that we will learn as we move ahead in the topic.
2000 has only twenty factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000.
Negative factors of 2000: Negative factors are nothing but the negative counterparts of the position factors of a number.
Since 2000 has twenty positive factors: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000, it will also have four negative counterparts, which are -1, -2, -3, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -125, -200, -250, -400, -500, -1000, and -2000.
Prime factors of 2000: Since 2000 is a composite number, it has 2 and 5 as its prime factor.
Prime factorization of 2000:Prime factorization of a number is the method of expressing 2000 as a product of prime factors.
The prime factorization of 2000 = 24 × 53
How to find the factors of 2000
There are several ways of finding factors of 2000. We will learn about them one by one as we go on.
Finding factors using multiplication
In this method, we will try to find such a pair of numbers that will give 2000 as their product. We recommend that you should follow the following steps to find factors using multiplication.
Step 1: Always look for a pair of numbers whose product is 2000.
Step 2: After finding such pairs, list them all one by one.
Here, factor pairs of 2000 are (1, 2000), (2, 1000), (4, 500), (5, 400), (8, 250), (10, 200), (16,125), (20,100), (25, 80), and (20,100).
So the factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000
Finding factors by division method
In the method, we need to find such numbers that divide 2000 completely without leaving any remainder.
2000/1 = 2000
2000/ 2 =1000
2000/ 4 =500
2000/ 5 = 400
2000/ 8 = 250
2000/ 10 = 200
2000/ 16 = 125
2000/ 20 = 100
2000/ 25 = 80
2000/ 40 = 50
2000/ 50 = 40
2000/ 80= 25
2000/ 100 = 20
2000/ 125 = 16
2000/ 200 = 10
2000/ 250 = 8
2000/ 400 = 5
2000/ 500 = 4
2000/ 1000 = 2
2000/ 2000 = 1
All the 16 numbers: 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, and 2000, mentioned above divide 2000 completely without any remainder. Hence, they are factors of 2000.
Prime Factors and Prime Factorization
In the prime factorization method, a number is expressed as the product of prime factors.
Here, as we know, 2000 = 24× 33
2 and 3 are the prime factors when multiplied together will give 2000 as a product of the multiplication.
Factor tree
A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
Factor Pairs
The factor pairs of a number refer to a pair of numbers which, when multiplied, will give the number as a product.
The factor pairs of 2000 are (1, 2000), (2, 1000), (4, 500), (5, 400), (8, 250), (10, 200), (16,125), (20,100), (25, 80), and (20,100).
Positive Pair Factors of 2000 are (1, 2000), (2, 1000), (4, 500), (5, 400), (8, 250), (10, 200), (16,125), (20,100), (25, 80), and (20,100).
Negative Pair Factors of 2000 are (-1, -2000), (-2, -1000), (-4, -500), (-5, -400), (-8, -250), (-10, -200), (-16, -125), (-20, -100), (-25, -80), and (-20, -100).
Common Mistakes and How to Avoid Them in Factors Of 2000
There are some errors that a child is bound to commit while discovering the factors of 2000. Let us know what error a child is likely to commit.
Mistake 1
A child might consider only the prime factors and leave other factors.
A child must know that a number has both prime and composite factors.
Factors of 2000 examples
Problem 1
If b × y = 2000 and b + y = 30, then find b and y.
The value of b can be 20 or 10 and the value of y can also be 20 or 10.
Explanation
We will first try to solve the sum of b and y = 30. Here, b can have either 10 or 20 and y can also have the same value. It means 10 + 20 = 30 or 20 + 10 = 30. So, the value we get here is 10 and 20 for each value, and the product of these values also equals 2000.
Problem 2
Find the remainder when 2000 is multiplied with 24.
The remainder that we are left with when we divide 2000 by 24 is 8.
Explanation
Divide 2000 by 24 to get 83 as quotient and 8 as its remainder.
Problem 3
Find the values of x and y, if 2000= 2^x × 5^y.
x = 4 and y = 3.
Explanation
We know that 24 multiplied with 53 gives 2000. So, the value of x and y will be 4 and 3 respectively.
Problem 4
Show the product of distinct prime factors of 2000.
10 is the product of two distinct prime factors of 2000.
Explanation
2 and 5 are the distinct prime factors of 2000 and their product is 10.
Problem 5
Verify if the smallest and largest factor of 2000 are divisible by 30.
The smallest factor 1 is not divisible by 30 and the largest factor 2000 is also not divisible by 30.
Explanation
Both the numbers 1 and 2000 are not divisible by 30 because they are not divisible by 3.
FAQs on factors of 2000
1.Mention two factors of 2000 whose product is 2000 ?
2.Name the person who discovered the square root.
3.Can you tell why the square root of 2 is irrational?
4.Can you find the square root of a negative number?
5. What can be called the principal root of the number?
Important Glossaries for Factors of 2000
- Prime Numbers: Those numbers which have no other factors other than 1 & the number itself.
- Composite Numbers: Those numbers that have more than 2 factors.
- Negative Factors: These are the counterparts of the positive factors of a number.
- Prime Factorization: Process of breaking down a composite number into products of several of its prime factors.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
