How many composite factors does 84 have?

2 Answers
Apr 25, 2018

8 composite factors.

Explanation:

We would need to list all the factors of 84 first.

This is easier than it sounds. Factors are always in pairs, so if you know one of the pair you can divide that factor into 84 to find the other,

Half of the factors are less than sqrt84 and are paired with factors greater than sqrt84

sqrt84 = 9. ....

Consider the numbers from 1" to " 9 .Which are factors?

1," "2," "3," "4," "6," "7" " are all factors.

Find the matching factors:

1," "2," "3," "4," "6," "7," "12," "14," "21," "28," "42," "84
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There are 12 factors. Of those, 1," "2," "3," "7 are not composite because they have less than 3 factors.

Therefore there are 12-4=8 composite factors

Apr 25, 2018

8.
The factors are 4, 6, 12, 14, 21, 28, 42, 84

Explanation:

Given 84=2^2*3*7

84 has a few factors, as shown:

84
=1*84
=2*42
=3*28
=4*21
=6*14
=7*12

Excluding 1 and the prime factors 2, 3, 7,
The number of composite factors =12-4
=8

Method 2:
Total number of composite factors
=total number of factors - total number of prime and unclassified factors
=(2+1)(1+1)(1+1)-1-3
=12-4
=8

Note: Total number of factors can be counted by multiplying the values of one added to the power of the primes.
i.e. Number of factors of a^xb^yc^z
=(x+1)(y+1)(z+1)