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The number of prime factors of (6)^10 x (7)^17 x (55)^27 is

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AnkitK
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The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   26 Mar 2011, 01:28
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The number of prime factors of \((6)^{10} x (7)^{17} x (55)^{27}\) is

a. 54
b. 64
c. 81
d. 91

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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   26 Mar 2011, 01:36
AnkitK wrote:
The number of prime factors of (6)^10 x (7)^17 x (55)^27 is
a. 54
b. 64
c. 81
d. 91


\((6)^{10} * (7)^{17} * (55)^{27}\)
\((2*3)^{10} * (7)^{17} * (5*11)^{27}\)
\(2^{10}*3^{10}*7^{17}*5^{27}*11^{27}\) Note: \((x*y)^k=x^k*y^k\)

Just add the powers:
10+10+17+27+27=91

Ans: "d"
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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   26 Mar 2011, 04:28
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AnkitK wrote:
The number of prime factors of (6)^10 x (7)^17 x (55)^27 is
a. 54
b. 64
c. 81
d. 91


Something wrong with the answer choices here. The number of PRIME factors is only 5 namely - 2,3,5,7 and 11. Every other factor (apart from 1) is a combination of two or more of these prime factors and is NOT a prime.
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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   27 Mar 2011, 06:39
6^10= (2x3)^10- 2 10 times, 3 10 times- 20
7^17= 7 -17 times
55^27= (5x11)^27- 5 27 times, 11 27 times

Total- 20+17+27+27= 91
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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   23 Apr 2020, 21:43
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Hi ,

I believe the question itself is wrong .
If it would have been to find out the total number of factors then we would have added 1 to each of the prime factor and at last would have multiplied all to get the answer .

Say , total number of factors of 6
6 = (2^1). (3^1)

So the total number of factors would be
(1+1).(1+1) = 4
And that’s the fact ,6 = 1,2,3,6

To find the total number of prime factors of 6
We would just consider the distinct prime factors of 6 -> 2 and 3 ———- that’s why we have two prime factors for 6.

Experts , kindly let me know whether my understanding is correct or not Bunuel chetan2u VeritasKarishma egmat

Posted from my mobile device
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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   23 Apr 2020, 22:10
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LeenaSai wrote:
Hi ,

I believe the question itself is wrong .
If it would have been to find out the total number of factors then we would have added 1 to each of the prime factor and at last would have multiplied all to get the answer .

Say , total number of factors of 6
6 = (2^1). (3^1)

So the total number of factors would be
(1+1).(1+1) = 4
And that’s the fact ,6 = 1,2,3,6

To find the total number of prime factors of 6
We would just consider the distinct prime factors of 6 -> 2 and 3 ———- that’s why we have two prime factors for 6.

Experts , kindly let me know whether my understanding is correct or not Bunuel chetan2u VeritasKarishma egmat

Posted from my mobile device


The question is very poorly constructed.
The prime factors of 36 will only be two - 2 and 3. It will not be 2,2,3,3.

You are correct in your understanding.
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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink] New post   23 Apr 2020, 22:12
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chetan2u wrote:
LeenaSai wrote:
Hi ,

I believe the question itself is wrong .
If it would have been to find out the total number of factors then we would have added 1 to each of the prime factor and at last would have multiplied all to get the answer .

Say , total number of factors of 6
6 = (2^1). (3^1)

So the total number of factors would be
(1+1).(1+1) = 4
And that’s the fact ,6 = 1,2,3,6

To find the total number of prime factors of 6
We would just consider the distinct prime factors of 6 -> 2 and 3 ———- that’s why we have two prime factors for 6.

Experts , kindly let me know whether my understanding is correct or not Bunuel chetan2u VeritasKarishma egmat

Posted from my mobile device


The question is very poorly constructed.
The prime factors of 36 will only be two - 2 and 3. It will not be 2,2,3,3.

You are correct in your understanding.




Thankuuuu for your response :)

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Re: The number of prime factors of (6)^10 x (7)^17 x (55)^27 is [#permalink]
23 Apr 2020, 22:12
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