How many factors of 60^2 are multiples of 3 ?

Question

A. 10
B. 12
C. 15
D. 20
E. 30

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gchandana · Answer

60^2 = 2^4 * 3^2 * 5^2 (prime factorization)

We calculate the total number of factors as = (a+1)(b+1)(c+1), where a, b, and c are powers of each prime number in prime factorized form. And we take +1 to consider the cases when that prime is raised to power 0, to include 1 and other cases where that prime isn't included (for example, we could have a factor 15 or 45, which doesn't include 2, so we shouldn't miss it out).

To calculate factors which are 3 multiples = (4+1)(2)(2+1), we don't take +1 for 3's power, as we want 3 to be there in all those factors.
Which gives 30 as the answer. Option E.

Hope it helps!

Praful_0810 · Answer

How many factors of 60^2 are multiples of 3 ?

Converting 60^2 into prime factorization - 2^4 * 3^2 * 5^2
So Total # factors = (4+1)*(2+1)*(2+1) = 45. 
However, we cannot consider 3^0 as this will give us factor which will not be multiple of 3.
So total # factors which are multiple of 3 are   (4+1)*(2)*(2+1) = 30   nos.

So option  E  is correct answer.

shivani1351 · Answer

60^2 = 3600
Prime Factorizarion of 3600 => 3^2 * 5^2 * 2^4

Now, for finding out the number of factors of 60^2 that are multiples of 3, we will have to ensure that there is atleast 1 multiple of 3 (except for this, there is no other constraint as such)

Hence, total number of such factors = 2*3*5 = 30 (Option E)

007Phoenix007 · Answer

Prime factorization of 60^2:
(2×3×2×5)^2 = 2^4×3^2×5^2

Now the total no of factors are:
(4+1)(2+1)(2+1)= 45
But we want all the factors of 3 
So we need to subtract the factors of 3^0
5×1×3=15

Therefore we get =45-15 =30

Hence option E

Dereno · Answer

60^2 = 60*60 = 2*3*2*5*2*3*2*5 = 2^4 * 3^2 * 5^2

Multiple of 3 = 3* ( 2^4 * 3 * 5^2) = 3*K

The number of factors of ( 2^4 * 3 * 5^2)

= (4+1)*(1+1)*(2+1)

= 5*2*3

=  30

Option E

ExpertsGlobal5 · Answer

Video explanation: 
 
 https://www.youtube.com/watch?v=uBsFl84sL9Y

impeditrem · Answer

factor multiple of 3 = Total factor - factors not a multiple of 3

factors not a multiple of 3

factors of  2^4 * 5^2 = 5 * 3 = 15 factors

Total factors

3^2 2^4 * 5^2 = 3* 5 * 3 = 45 factors

45 - 15 = 30 factors (option e)

How many factors of 60^2 are multiples of 3 ?

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How many factors of 60^2 are multiples of 3 ?

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