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How many distinct factors do 165 and 300 have in common?

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by Jay@ManhattanReview » Thu Sep 12, 2019 8:51 pm
BTGmoderatorDC wrote:How many distinct factors do 165 and 300 have in common?

A. 2
B. 3
C. 4
D. 5
E. 8

OA C

Source: Veritas Prep
165 = 1*3*5*11; and
330 = 1*2^2*3*5^2

We see that 1, 3 and 5 are common factors; however, one more factor is 15 (= 3*5). So there are 4 distinct common factors.

Another approach to this question:

We know that the Highest Common Factor/Greatest Common Divisor to two numbers is called GCD or HCF. Thus, let's find out GCD/HCF of 165 and 330.

GCD (165 & 330) = 15

Since GCD is 15, all the factors of 15 would be common to 165 and 330.

All factors of 15 are 1, 3, 5, and 15. There are four factors.

The correct answer: C

Hope this helps!

-Jay
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by swerve » Sat Sep 14, 2019 2:38 am
BTGmoderatorDC wrote:How many distinct factors do 165 and 300 have in common?

A. 2
B. 3
C. 4
D. 5
E. 8

OA C

Source: Veritas Prep
When prime-factorized \(165=3\cdot 5 \cdot 11\) and \(300=2^3 \cdot 3 \cdot 5^2\)

The common factors of the numbers 165 and 300 are 3 and 5.

Since we have been asked to find the distinct common factors, they will be 1, 3, 5 and \(3\cdot 5 (15)\) which is 4. \(\Rightarrow \) __C__
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by Scott@TargetTestPrep » Wed Sep 18, 2019 8:50 am
BTGmoderatorDC wrote:How many distinct factors do 165 and 300 have in common?

A. 2
B. 3
C. 4
D. 5
E. 8

OA C

Source: Veritas Prep
165 = 5 x 33 = 5 x 11 x 3

300 = 12 x 25 = 2^2 x 3 x 5^2

Thus, the factors in common are 1, 3, 5, 15. (Recall that 1 is a factor of every number, even though it doesn't play a role in the prime factorization of a number since it is not prime.)

Answer: C

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