1. Steps to find factors of 800 using Division Method

Example: Find factors of 800

  • Divide 800 by 1: 800 ÷ 1 : Remainder = 0
  • Divide 800 by 2: 800 ÷ 2 : Remainder = 0
  • Divide 800 by 4: 800 ÷ 4 : Remainder = 0
  • Divide 800 by 5: 800 ÷ 5 : Remainder = 0
  • Divide 800 by 8: 800 ÷ 8 : Remainder = 0
  • Divide 800 by 10: 800 ÷ 10 : Remainder = 0
  • Divide 800 by 16: 800 ÷ 16 : Remainder = 0
  • Divide 800 by 20: 800 ÷ 20 : Remainder = 0
  • Divide 800 by 25: 800 ÷ 25 : Remainder = 0
  • Divide 800 by 32: 800 ÷ 32 : Remainder = 0
  • Divide 800 by 40: 800 ÷ 40 : Remainder = 0
  • Divide 800 by 50: 800 ÷ 50 : Remainder = 0
  • Divide 800 by 80: 800 ÷ 80 : Remainder = 0
  • Divide 800 by 100: 800 ÷ 100 : Remainder = 0
  • Divide 800 by 160: 800 ÷ 160 : Remainder = 0
  • Divide 800 by 200: 800 ÷ 200 : Remainder = 0
  • Divide 800 by 400: 800 ÷ 400 : Remainder = 0
  • Divide 800 by 800: 800 ÷ 800 : Remainder = 0

Hence, Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, and 800

2. Steps to find factors of 800 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 800 using the division method, follow these steps:

  • Step 1. Start dividing 800 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 800, which is 2. Divide 800 by 2 to obtain the quotient (400).
    800 ÷ 2 = 400
  • Step 3. Repeat step 1 with the obtained quotient (400).
    400 ÷ 2 = 200
    200 ÷ 2 = 100
    100 ÷ 2 = 50
    50 ÷ 2 = 25
    25 ÷ 5 = 5
    5 ÷ 5 = 1

So, the prime factorization of 800 is, 800 = 2 x 2 x 2 x 2 x 2 x 5 x 5.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 800 as shown below:

So, the prime factorization of 800 is, 800 = 2 x 2 x 2 x 2 x 2 x 5 x 5.

3. Find factors of 800 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 800 would be the two numbers which, when multiplied, give 800 as the result.

The following table represents the calculation of factors of 800 in pairs:

Factor Pair Pair Factorization
1 and 800 1 x 800 = 800
2 and 400 2 x 400 = 800
4 and 200 4 x 200 = 800
5 and 160 5 x 160 = 800
8 and 100 8 x 100 = 800
10 and 80 10 x 80 = 800
16 and 50 16 x 50 = 800
20 and 40 20 x 40 = 800
25 and 32 25 x 32 = 800

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 800. They are called negative pair factors.

Hence, the negative pairs of 800 would be ( -1 , -800 ) , ( -2 , -400 ) , ( -4 , -200 ) , ( -5 , -160 ) , ( -8 , -100 ) , ( -10 , -80 ) , ( -16 , -50 ) , ( -20 , -40 ) and ( -25 , -32 ) .

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. 800 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 800.
  • Every number is a factor of zero (0), since 800 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, 32, 40, 50, 80, 100, 160, 200, 400, 800 are exact divisors of 800.
  • Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800. Each factor divides 800 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, 32, 40, 50, 80, 100, 160, 200, 400, 800 are all less than or equal to 800.

Frequently Asked Questions

  • What is prime factorization of 800?

    Prime factorization of 800 is 2 x 2 x 2 x 2 x 2 x 5 x 5.

  • How do you find factors of a negative number? ( eg. -800 )?

    Factors of -800 are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400, -800.

  • What are the prime factors of 800?

    The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
    Prime factors of 800 are 2, 2, 2, 2, 2, 5, 5.

  • What are pair factors of 800?

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

  • What is the greatest prime factors of 800?

    The greatest prime factor of 800 is 5.

  • What are six multiples of 800?

    First five multiples of 800 are 1600, 2400, 3200, 4000, 4800, 5600.

  • What are factors of 800?

    Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.

  • Which is the smallest prime factor of 800?

    Smallest prime factor of 800 is 2.

  • Is 800 a whole number?

    Yes 800 is a whole number.

Examples of Factors

Kevin has been asked to write 17 factor(s) of 800. Can you predict the answer?

17 factor(s) of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400.

Sammy is puzzled while calculating the prime factors of 800. Can you help him find them?

Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
Prime factors of 800 are 2, 2, 2, 2, 2, 5, 5

What is prime factorization of 800?

Prime factorization of 800 is 2 x 2 x 2 x 2 x 2 x 5 x 5 = 25 x 52.

Ariel has been assigned the task to find the product of all the prime factors of 800. Can you help her?

Prime factors of 800 are 2, 2, 2, 2, 2, 5, 5.
Hence, the product of prime factors of 10.

Can you help Rubel to find out the product of the even factors of 800?

Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
Even factors of 800 are 2, 4, 8, 10, 16, 20, 32, 40, 50, 80, 100, 160, 200, 400, 800.
Hence, product of even factors of 800 is; 2 x 4 x 8 x 10 x 16 x 20 x 32 x 40 x 50 x 80 x 100 x 160 x 200 x 400 x 800 = 1.073741824e+24.

Joy wants to calculate mean of all the factors of 800. Help him in finding the mean of 800.

Factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 800 is 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 80 + 100 + 160 + 200 + 400 + 800 = 1953.
Hence, the mean of factors of 800 is 1953 ÷ 18 = 108.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 800? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800.
Negative factors are -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -80, -100, -160, -200, -400, -800.