Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000

How to find factors of a number

1. Steps to find factors of 10000 using Division Method

Example: Find factors of 10000

  • Divide 10000 by 1: 10000 ÷ 1 : Remainder = 0
  • Divide 10000 by 2: 10000 ÷ 2 : Remainder = 0
  • Divide 10000 by 4: 10000 ÷ 4 : Remainder = 0
  • Divide 10000 by 5: 10000 ÷ 5 : Remainder = 0
  • Divide 10000 by 8: 10000 ÷ 8 : Remainder = 0
  • Divide 10000 by 10: 10000 ÷ 10 : Remainder = 0
  • Divide 10000 by 16: 10000 ÷ 16 : Remainder = 0
  • Divide 10000 by 20: 10000 ÷ 20 : Remainder = 0
  • Divide 10000 by 25: 10000 ÷ 25 : Remainder = 0
  • Divide 10000 by 40: 10000 ÷ 40 : Remainder = 0
  • Divide 10000 by 50: 10000 ÷ 50 : Remainder = 0
  • Divide 10000 by 80: 10000 ÷ 80 : Remainder = 0
  • Divide 10000 by 100: 10000 ÷ 100 : Remainder = 0
  • Divide 10000 by 125: 10000 ÷ 125 : Remainder = 0
  • Divide 10000 by 200: 10000 ÷ 200 : Remainder = 0
  • Divide 10000 by 250: 10000 ÷ 250 : Remainder = 0
  • Divide 10000 by 400: 10000 ÷ 400 : Remainder = 0
  • Divide 10000 by 500: 10000 ÷ 500 : Remainder = 0
  • Divide 10000 by 625: 10000 ÷ 625 : Remainder = 0
  • Divide 10000 by 1000: 10000 ÷ 1000 : Remainder = 0
  • Divide 10000 by 1250: 10000 ÷ 1250 : Remainder = 0
  • Divide 10000 by 2000: 10000 ÷ 2000 : Remainder = 0
  • Divide 10000 by 2500: 10000 ÷ 2500 : Remainder = 0
  • Divide 10000 by 5000: 10000 ÷ 5000 : Remainder = 0
  • Divide 10000 by 10000: 10000 ÷ 10000 : Remainder = 0

Hence, Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000

2. Steps to find factors of 10000 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 10000 using the division method, follow these steps:

  • Step 1. Start dividing 10000 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
  • Step 2. After finding the smallest prime factor of the number 10000, which is 2. Divide 10000 by 2 to obtain the quotient (5000).
    10000 ÷ 2 = 5000
  • Step 3. Repeat step 1 with the obtained quotient (5000).
    5000 ÷ 2 = 2500
    2500 ÷ 2 = 1250
    1250 ÷ 2 = 625
    625 ÷ 5 = 125
    125 ÷ 5 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 10000 is, 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 10000 as shown below:

So, the prime factorization of 10000 is, 10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5.

3. Find factors of 10000 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 10000 would be the two numbers which, when multiplied, give 10000 as the result.

The following table represents the calculation of factors of 10000 in pairs:

Factor Pair Pair Factorization
1 and 10000 1 x 10000 = 10000
2 and 5000 2 x 5000 = 10000
4 and 2500 4 x 2500 = 10000
5 and 2000 5 x 2000 = 10000
8 and 1250 8 x 1250 = 10000
10 and 1000 10 x 1000 = 10000
16 and 625 16 x 625 = 10000
20 and 500 20 x 500 = 10000
25 and 400 25 x 400 = 10000
40 and 250 40 x 250 = 10000
50 and 200 50 x 200 = 10000
80 and 125 80 x 125 = 10000
100 and 100 100 x 100 = 10000

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 10000. They are called negative pair factors.

Hence, the negative pairs of 10000 would be ( -1 , -10000 ) , ( -2 , -5000 ) , ( -4 , -2500 ) , ( -5 , -2000 ) , ( -8 , -1250 ) , ( -10 , -1000 ) , ( -16 , -625 ) , ( -20 , -500 ) , ( -25 , -400 ) , ( -40 , -250 ) , ( -50 , -200 ) , ( -80 , -125 ) and ( -100 , -100 ) .

What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 10000 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 10000.
  • Every number is a factor of zero (0), since 10000 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000 are exact divisors of 10000.
  • Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000. Each factor divides 10000 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000 are all less than or equal to 10000.

Frequently Asked Questions

  • What are the prime factors of 10000?

    The factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
    Prime factors of 10000 are 2, 2, 2, 2, 5, 5, 5, 5.

  • What is the sum of all factors of 10000?

    The sum of all factors of 10000 is 24211.

  • What are the pair factors of 10000?

    Pair factors of 10000 are (1,10000), (2,5000), (4,2500), (5,2000), (8,1250), (10,1000), (16,625), (20,500), (25,400), (40,250), (50,200), (80,125), (100,100).

  • What two numbers make 10000?

    Two numbers that make 10000 are 2 and 5000.

  • What are multiples of 10000?

    First five multiples of 10000 are 20000, 30000, 40000, 50000.

  • Is 10000 a perfect square?

    Yes 10000 is a perfect square.

  • Which is greatest factor of 10000?

    The greatest factor of 10000 is 5000.

  • How do you factors of 10000?

    Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.

  • What are five multiples of 10000?

    First five multiples of 10000 are 20000, 30000, 40000, 50000, 60000.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 10000?

Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
Even factors of 10000 are 2, 4, 8, 10, 16, 20, 40, 50, 80, 100, 200, 250, 400, 500, 1000, 1250, 2000, 2500, 5000, 10000.
Hence, product of even factors of 10000 is; 2 x 4 x 8 x 10 x 16 x 20 x 40 x 50 x 80 x 100 x 200 x 250 x 400 x 500 x 1000 x 1250 x 2000 x 2500 x 5000 x 10000 = 1.0240000000000002e+43.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 10000? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -125, -200, -250, -400, -500, -625, -1000, -1250, -2000, -2500, -5000, -10000.

How many factors are there for 10000?

Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
So there are in total 25 factors.

Sammy is puzzled while calculating the prime factors of 10000. Can you help him find them?

Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
Prime factors of 10000 are 2, 2, 2, 2, 5, 5, 5, 5

Joey wants to write all the prime factors of 10000 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 10000 are 2, 2, 2, 2, 5, 5, 5, 5.
So in exponential form it can be written as 24 x 54.

What is prime factorization of 10000?

Prime factorization of 10000 is 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 = 24 x 54.

Can you help Rubel to find out the product of the even factors of 10000?

Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000.
Even factors of 10000 are 2, 4, 8, 10, 16, 20, 40, 50, 80, 100, 200, 250, 400, 500, 1000, 1250, 2000, 2500, 5000, 10000.
Hence, product of even factors of 10000 is; 2 x 4 x 8 x 10 x 16 x 20 x 40 x 50 x 80 x 100 x 200 x 250 x 400 x 500 x 1000 x 1250 x 2000 x 2500 x 5000 x 10000 = 1.0240000000000002e+43.