Q:

# What are the factors of 70?

A:

The factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70. They are the numbers that can be multiplied by one or more other numbers to get 70 as a product.

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Every natural number, except the numeral one, has itself and one as factors. As for the remaining factors of 70, one can find them by using successive division, in no particular order, to identify all numbers that divide into 70 without a remainder.

Another, more systematic, approach is to determine which numbers can be divided into 70 by starting with the smallest prime number and moving in succession to those that are larger. Since 70 can be divided by two exactly 35 times, 70’s first two factors are one and two.

The next prime number, which is three, does not divide into 70 evenly. However, the one that follows does. That number is five, and its corresponding factor is 14.

Seven is the last prime number that divides into 70 without a remainder. It is the first half of the factor pair completed by the number 10. Since there are no other primes that break up 70 evenly, the list of numbers comprising the factors of 70 is then complete.

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