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03 Jan 2022, 05:45
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Difficulty:
95%
(hard)
Question Stats:
47% (02:25) correct
53%
(02:10)
wrong
based on 194
sessions
History
Date
Time
Result
Not Attempted Yet
What is the highest integer power of 288 that can divide 55! ?
A. 13
B. 11
C. 10
D. 26
E. 50
Are You Up For the Challenge: 700 Level Questions
A. 13
B. 11
C. 10
D. 26
E. 50
Are You Up For the Challenge: 700 Level Questions
03 Jan 2022, 07:36
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I think the answer is 10.
288 = 2^5 * 3^2
2^5 > 3^2
55! contains 27*2^1, 13*2^2, 6* 2^3, 3* 2^4, 1* 2^5.
Summing the number of 2^x together, we get 50 in total.
Since 5k <= 50, k =10
288 = 2^5 * 3^2
2^5 > 3^2
55! contains 27*2^1, 13*2^2, 6* 2^3, 3* 2^4, 1* 2^5.
Summing the number of 2^x together, we get 50 in total.
Since 5k <= 50, k =10
03 Jan 2022, 11:06
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Hi Bunuel,
Thanks for posting the question. I have restarted my prep after quite some time. But, I remember questions like these require us to calculate the greatest integer function. In this case, it is asked the highest power of 288 that can divide 55!. So, first, we begin with prime factorizing 288.
288 = 2^5 X 3^2, it has two prime factors
now we use the GIF using the prime factors 2 and 3
Using 2
=[55/2] + [55/2^2] + [55/2^3] + [55/2^4] + [55/2^5]
= 27 + 13 + 6 + 3 + 1
= 50 no of factors of 2 in 55!
Using 3
=[55/3] + [55/3^2] + [55/3^3]
= 18 + 6 + 2
=26 no of factors of 3 in 55!
Since the minimum out of those two factors is 26, does it mean the answer is 26? D?
Not sure if we have any follow-up steps.
Regards,
RK
Thanks for posting the question. I have restarted my prep after quite some time. But, I remember questions like these require us to calculate the greatest integer function. In this case, it is asked the highest power of 288 that can divide 55!. So, first, we begin with prime factorizing 288.
288 = 2^5 X 3^2, it has two prime factors
now we use the GIF using the prime factors 2 and 3
Using 2
=[55/2] + [55/2^2] + [55/2^3] + [55/2^4] + [55/2^5]
= 27 + 13 + 6 + 3 + 1
= 50 no of factors of 2 in 55!
Using 3
=[55/3] + [55/3^2] + [55/3^3]
= 18 + 6 + 2
=26 no of factors of 3 in 55!
Since the minimum out of those two factors is 26, does it mean the answer is 26? D?
Not sure if we have any follow-up steps.
Regards,
RK
