Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, and 2800

How to find factors of a number

1. Steps to find factors of 2800 using Division Method

Example: Find factors of 2800

  • Divide 2800 by 1: 2800 ÷ 1 : Remainder = 0
  • Divide 2800 by 2: 2800 ÷ 2 : Remainder = 0
  • Divide 2800 by 4: 2800 ÷ 4 : Remainder = 0
  • Divide 2800 by 5: 2800 ÷ 5 : Remainder = 0
  • Divide 2800 by 7: 2800 ÷ 7 : Remainder = 0
  • Divide 2800 by 8: 2800 ÷ 8 : Remainder = 0
  • Divide 2800 by 10: 2800 ÷ 10 : Remainder = 0
  • Divide 2800 by 14: 2800 ÷ 14 : Remainder = 0
  • Divide 2800 by 16: 2800 ÷ 16 : Remainder = 0
  • Divide 2800 by 20: 2800 ÷ 20 : Remainder = 0
  • Divide 2800 by 25: 2800 ÷ 25 : Remainder = 0
  • Divide 2800 by 28: 2800 ÷ 28 : Remainder = 0
  • Divide 2800 by 35: 2800 ÷ 35 : Remainder = 0
  • Divide 2800 by 40: 2800 ÷ 40 : Remainder = 0
  • Divide 2800 by 50: 2800 ÷ 50 : Remainder = 0
  • Divide 2800 by 56: 2800 ÷ 56 : Remainder = 0
  • Divide 2800 by 70: 2800 ÷ 70 : Remainder = 0
  • Divide 2800 by 80: 2800 ÷ 80 : Remainder = 0
  • Divide 2800 by 100: 2800 ÷ 100 : Remainder = 0
  • Divide 2800 by 112: 2800 ÷ 112 : Remainder = 0
  • Divide 2800 by 140: 2800 ÷ 140 : Remainder = 0
  • Divide 2800 by 175: 2800 ÷ 175 : Remainder = 0
  • Divide 2800 by 200: 2800 ÷ 200 : Remainder = 0
  • Divide 2800 by 280: 2800 ÷ 280 : Remainder = 0
  • Divide 2800 by 350: 2800 ÷ 350 : Remainder = 0
  • Divide 2800 by 400: 2800 ÷ 400 : Remainder = 0
  • Divide 2800 by 560: 2800 ÷ 560 : Remainder = 0
  • Divide 2800 by 700: 2800 ÷ 700 : Remainder = 0
  • Divide 2800 by 1400: 2800 ÷ 1400 : Remainder = 0
  • Divide 2800 by 2800: 2800 ÷ 2800 : Remainder = 0

Hence, Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, and 2800

2. Steps to find factors of 2800 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 2800 using the division method, follow these steps:

  • Step 1. Start dividing 2800 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 2800, which is 2. Divide 2800 by 2 to obtain the quotient (1400).
    2800 ÷ 2 = 1400
  • Step 3. Repeat step 1 with the obtained quotient (1400).
    1400 ÷ 2 = 700
    700 ÷ 2 = 350
    350 ÷ 2 = 175
    175 ÷ 5 = 35
    35 ÷ 5 = 7
    7 ÷ 7 = 1

So, the prime factorization of 2800 is, 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 2800 as shown below:

So, the prime factorization of 2800 is, 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7.

3. Find factors of 2800 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 2800 would be the two numbers which, when multiplied, give 2800 as the result.

The following table represents the calculation of factors of 2800 in pairs:

Factor Pair Pair Factorization
1 and 2800 1 x 2800 = 2800
2 and 1400 2 x 1400 = 2800
4 and 700 4 x 700 = 2800
5 and 560 5 x 560 = 2800
7 and 400 7 x 400 = 2800
8 and 350 8 x 350 = 2800
10 and 280 10 x 280 = 2800
14 and 200 14 x 200 = 2800
16 and 175 16 x 175 = 2800
20 and 140 20 x 140 = 2800
25 and 112 25 x 112 = 2800
28 and 100 28 x 100 = 2800
35 and 80 35 x 80 = 2800
40 and 70 40 x 70 = 2800
50 and 56 50 x 56 = 2800

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 2800. They are called negative pair factors.

Hence, the negative pairs of 2800 would be ( -1 , -2800 ) , ( -2 , -1400 ) , ( -4 , -700 ) , ( -5 , -560 ) , ( -7 , -400 ) , ( -8 , -350 ) , ( -10 , -280 ) , ( -14 , -200 ) , ( -16 , -175 ) , ( -20 , -140 ) , ( -25 , -112 ) , ( -28 , -100 ) , ( -35 , -80 ) , ( -40 , -70 ) and ( -50 , -56 ) .

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. 2800 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 2800.
  • Every number is a factor of zero (0), since 2800 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, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800 are exact divisors of 2800.
  • Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800. Each factor divides 2800 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800 are all less than or equal to 2800.

Frequently Asked Questions

  • What are the prime factors of 2800?

    The factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
    Prime factors of 2800 are 2, 2, 2, 2, 5, 5, 7.

  • What is the sum of all factors of 2800?

    The sum of all factors of 2800 is 7688.

  • What are the pair factors of 2800?

    Pair factors of 2800 are (1,2800), (2,1400), (4,700), (5,560), (7,400), (8,350), (10,280), (14,200), (16,175), (20,140), (25,112), (28,100), (35,80), (40,70), (50,56).

  • What two numbers make 2800?

    Two numbers that make 2800 are 2 and 1400.

  • What are multiples of 2800?

    First five multiples of 2800 are 5600, 8400, 11200, 14000.

  • Is 2800 a perfect square?

    No 2800 is not a perfect square.

  • Which is greatest factor of 2800?

    The greatest factor of 2800 is 1400.

  • How do you factors of 2800?

    Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.

  • What are five multiples of 2800?

    First five multiples of 2800 are 5600, 8400, 11200, 14000, 16800.

Examples of Factors

Can you help Rubel to find out the product of the even factors of 2800?

Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
Even factors of 2800 are 2, 4, 8, 10, 14, 16, 20, 28, 40, 50, 56, 70, 80, 100, 112, 140, 200, 280, 350, 400, 560, 700, 1400, 2800.
Hence, product of even factors of 2800 is; 2 x 4 x 8 x 10 x 14 x 16 x 20 x 28 x 40 x 50 x 56 x 70 x 80 x 100 x 112 x 140 x 200 x 280 x 350 x 400 x 560 x 700 x 1400 x 2800 = 9.51166013805414e+44.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 2800? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
Negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -25, -28, -35, -40, -50, -56, -70, -80, -100, -112, -140, -175, -200, -280, -350, -400, -560, -700, -1400, -2800.

How many factors are there for 2800?

Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
So there are in total 30 factors.

Sammy is puzzled while calculating the prime factors of 2800. Can you help him find them?

Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
Prime factors of 2800 are 2, 2, 2, 2, 5, 5, 7

Joey wants to write all the prime factors of 2800 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 2800 are 2, 2, 2, 2, 5, 5, 7.
So in exponential form it can be written as 24 x 52 x 7.

What is prime factorization of 2800?

Prime factorization of 2800 is 2 x 2 x 2 x 2 x 5 x 5 x 7 = 24 x 52 x 7.

Can you help Rubel to find out the product of the even factors of 2800?

Factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
Even factors of 2800 are 2, 4, 8, 10, 14, 16, 20, 28, 40, 50, 56, 70, 80, 100, 112, 140, 200, 280, 350, 400, 560, 700, 1400, 2800.
Hence, product of even factors of 2800 is; 2 x 4 x 8 x 10 x 14 x 16 x 20 x 28 x 40 x 50 x 56 x 70 x 80 x 100 x 112 x 140 x 200 x 280 x 350 x 400 x 560 x 700 x 1400 x 2800 = 9.51166013805414e+44.