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
 

There are several ways of finding factors of 2000. We will learn about them one by one as we go on.
 

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
 

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.

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.
 

A factor tree is a graphical representation of factors of any number. In the diagram, each branch represents the prime factors a number has.
 

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).
 

• 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.