Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840

How to find factors of a number

1. Steps to find factors of 840 using Division Method

Example: Find factors of 840

  • Divide 840 by 1: 840 ÷ 1 : Remainder = 0
  • Divide 840 by 2: 840 ÷ 2 : Remainder = 0
  • Divide 840 by 3: 840 ÷ 3 : Remainder = 0
  • Divide 840 by 4: 840 ÷ 4 : Remainder = 0
  • Divide 840 by 5: 840 ÷ 5 : Remainder = 0
  • Divide 840 by 6: 840 ÷ 6 : Remainder = 0
  • Divide 840 by 7: 840 ÷ 7 : Remainder = 0
  • Divide 840 by 8: 840 ÷ 8 : Remainder = 0
  • Divide 840 by 10: 840 ÷ 10 : Remainder = 0
  • Divide 840 by 12: 840 ÷ 12 : Remainder = 0
  • Divide 840 by 14: 840 ÷ 14 : Remainder = 0
  • Divide 840 by 15: 840 ÷ 15 : Remainder = 0
  • Divide 840 by 20: 840 ÷ 20 : Remainder = 0
  • Divide 840 by 21: 840 ÷ 21 : Remainder = 0
  • Divide 840 by 24: 840 ÷ 24 : Remainder = 0
  • Divide 840 by 28: 840 ÷ 28 : Remainder = 0
  • Divide 840 by 30: 840 ÷ 30 : Remainder = 0
  • Divide 840 by 35: 840 ÷ 35 : Remainder = 0
  • Divide 840 by 40: 840 ÷ 40 : Remainder = 0
  • Divide 840 by 42: 840 ÷ 42 : Remainder = 0
  • Divide 840 by 56: 840 ÷ 56 : Remainder = 0
  • Divide 840 by 60: 840 ÷ 60 : Remainder = 0
  • Divide 840 by 70: 840 ÷ 70 : Remainder = 0
  • Divide 840 by 84: 840 ÷ 84 : Remainder = 0
  • Divide 840 by 105: 840 ÷ 105 : Remainder = 0
  • Divide 840 by 120: 840 ÷ 120 : Remainder = 0
  • Divide 840 by 140: 840 ÷ 140 : Remainder = 0
  • Divide 840 by 168: 840 ÷ 168 : Remainder = 0
  • Divide 840 by 210: 840 ÷ 210 : Remainder = 0
  • Divide 840 by 280: 840 ÷ 280 : Remainder = 0
  • Divide 840 by 420: 840 ÷ 420 : Remainder = 0
  • Divide 840 by 840: 840 ÷ 840 : Remainder = 0

Hence, Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, and 840

2. Steps to find factors of 840 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 840 using the division method, follow these steps:

  • Step 1. Start dividing 840 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 840, which is 2. Divide 840 by 2 to obtain the quotient (420).
    840 ÷ 2 = 420
  • Step 3. Repeat step 1 with the obtained quotient (420).
    420 ÷ 2 = 210
    210 ÷ 2 = 105
    105 ÷ 3 = 35
    35 ÷ 5 = 7
    7 ÷ 7 = 1

So, the prime factorization of 840 is, 840 = 2 x 2 x 2 x 3 x 5 x 7.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 840 as shown below:

So, the prime factorization of 840 is, 840 = 2 x 2 x 2 x 3 x 5 x 7.

3. Find factors of 840 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 840 would be the two numbers which, when multiplied, give 840 as the result.

The following table represents the calculation of factors of 840 in pairs:

Factor Pair Pair Factorization
1 and 840 1 x 840 = 840
2 and 420 2 x 420 = 840
3 and 280 3 x 280 = 840
4 and 210 4 x 210 = 840
5 and 168 5 x 168 = 840
6 and 140 6 x 140 = 840
7 and 120 7 x 120 = 840
8 and 105 8 x 105 = 840
10 and 84 10 x 84 = 840
12 and 70 12 x 70 = 840
14 and 60 14 x 60 = 840
15 and 56 15 x 56 = 840
20 and 42 20 x 42 = 840
21 and 40 21 x 40 = 840
24 and 35 24 x 35 = 840
28 and 30 28 x 30 = 840

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 840. They are called negative pair factors.

Hence, the negative pairs of 840 would be ( -1 , -840 ) , ( -2 , -420 ) , ( -3 , -280 ) , ( -4 , -210 ) , ( -5 , -168 ) , ( -6 , -140 ) , ( -7 , -120 ) , ( -8 , -105 ) , ( -10 , -84 ) , ( -12 , -70 ) , ( -14 , -60 ) , ( -15 , -56 ) , ( -20 , -42 ) , ( -21 , -40 ) , ( -24 , -35 ) and ( -28 , -30 ) .

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. 840 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 840.
  • Every number is a factor of zero (0), since 840 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, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840 are exact divisors of 840.
  • Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840. Each factor divides 840 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840 are all less than or equal to 840.

Frequently Asked Questions

  • What are the prime factors of 840?

    The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
    Prime factors of 840 are 2, 2, 2, 3, 5, 7.

  • What two numbers make 840?

    Two numbers that make 840 are 2 and 420.

  • What is the greatest prime factors of 840?

    The greatest prime factor of 840 is 7.

  • What are factors of 840?

    Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.

  • How do you find factors of a negative number? ( eg. -840 )?

    Factors of -840 are -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -28, -30, -35, -40, -42, -56, -60, -70, -84, -105, -120, -140, -168, -210, -280, -420, -840.

  • What are five multiples of 840?

    First five multiples of 840 are 1680, 2520, 3360, 4200, 5040.

  • Write some multiples of 840?

    First five multiples of 840 are 1680, 2520, 3360, 4200.

  • Is 840 a perfect square?

    No 840 is not a perfect square.

  • What two numbers make 840?

    Two numbers that make 840 are 2 and 420.

Examples of Factors

What is prime factorization of 840?

Prime factorization of 840 is 2 x 2 x 2 x 3 x 5 x 7 = 23 x 3 x 5 x 7.

Sammy is puzzled while calculating the prime factors of 840. Can you help him find them?

Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
Prime factors of 840 are 2, 2, 2, 3, 5, 7

Kevin has been asked to write 31 factor(s) of 840. Can you predict the answer?

31 factor(s) of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420.

Joey wants to write all the prime factors of 840 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 840 are 2, 2, 2, 3, 5, 7.
So in exponential form it can be written as 23 x 3 x 5 x 7.

How many factors are there for 840?

Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
So there are in total 32 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 840? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
Negative factors are -1, -2, -3, -4, -5, -6, -7, -8, -10, -12, -14, -15, -20, -21, -24, -28, -30, -35, -40, -42, -56, -60, -70, -84, -105, -120, -140, -168, -210, -280, -420, -840.

Can you help Rubel to find out the product of the even factors of 840?

Factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.
Even factors of 840 are 2, 4, 6, 8, 10, 12, 14, 20, 24, 28, 30, 40, 42, 56, 60, 70, 84, 120, 140, 168, 210, 280, 420, 840.
Hence, product of even factors of 840 is; 2 x 4 x 6 x 8 x 10 x 12 x 14 x 20 x 24 x 28 x 30 x 40 x 42 x 56 x 60 x 70 x 84 x 120 x 140 x 168 x 210 x 280 x 420 x 840 = 5.0548861754276306e+38.