The factors of 840 are the numbers that divide 840 evenly without leaving a remainder. To find the factors, we start by determining the prime factorization of 840.
First, we can divide 840 by the smallest prime number, which is 2:
- 840 ÷ 2 = 420
- 420 ÷ 2 = 210
- 210 ÷ 2 = 105
Now we can’t divide 105 by 2, so we move to the next prime number, which is 3:
- 105 ÷ 3 = 35
Next, we continue with 5, the next prime number:
- 35 ÷ 5 = 7
Now we are left with 7, which is a prime number as well. Thus, the prime factorization of 840 is:
- 2 × 2 × 2 × 3 × 5 × 7,
or in exponential form:
- 23 × 31 × 51 × 71
To find all factors of 840, we take all combinations of these prime factors. The complete list of factors includes:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 10
- 12
- 14
- 15
- 20
- 21
- 28
- 30
- 35
- 42
- 56
- 60
- 70
- 84
- 105
- 120
- 140
- 210
- 280
- 420
- 840
In summary, the factors of 840 are all the numbers that can multiply together to result in 840.