How many of the positive factors of 210 are not factors of 80?

Question

A. 6
B. 8
C. 10
D. 12
E. 14

GMATinsight · Accepted Answer

210 = 2^1*3^1*5^1*7^1 
 80 = 2^4*5

COmmon factors of 210 and 80 will be the factors of GCD of 80 and 210

GCD (80, 210)  = 2^1*5^1 = 10

Number of Factors   
  For a Number  N=a^p*b^q*c^r*...  where a, b, c etc are distinct prime factors of n and p, q r are their respective exponents
The number of factors of  N = (p+1)*(q+1)*(r+1)*...  and so on

Therefore,

Factors of 210 = (1+1)*(1+1)*(1+1)*(1+1) = 16

Factors of GCD = (1+1)*(1+1) = 4

Factors of 210 that are not factors of 80 = 16-4 = 12

Answer: Option D

sayan640 · Answer

GMATinsight  Can you please list down the numbers ?

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samarpan.g28 · Answer

210= 2^1 * 3^1 * 5^1 * 7^1  i.e. total (1+1)*(1+1)*(1+1)*(1+1)=16 factors {1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210}.

80= 2^4 * 5^1

The common factors of 210 and 80 are thus GCD(210,80) =  2^1  and  5^1  i.e. total (1+1)*(1+1)=4
Therefore, the factors of 210 which are not the factors of 80 are 16-4=12 {3,6,7,14,15,21,30,35,42,70,105,210}.
Option (D) is correct.

arnavislockedin · Answer

You can just find the combinations of prime factors of 210 that aren't within 1, 2, 5, 10 (for the GCD 10) so for example 2x5x7 = 70 is one of them.

How many of the positive factors of 210 are not factors of 80?

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How many of the positive factors of 210 are not factors of 80?

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