What is the highest power of 48 in 32!?
  • a)
    7
  • b)
    14
  • c)
    15
  • d)
    31
Correct answer is option 'A'. Can you explain this answer?

CAT Question

Chaitanya Ande
Jun 28, 2018
2^31 but 48 is 2^4×3 so (2^4)^7×3^something>7 so answer is

Ankita Tiwari
Jul 01, 2020
The answer should be 7 as 48=2^4 * 3 so 32! has 2^4 factors to approx 7 times and 32! has 3 factors upto 14 times .... so least(7,14) =7

Yathartha
Sep 10, 2020
Correct answer is A

Kamal Bhatt
Aug 24, 2019
It will be a only because 2ki power 31 has 7 ,,16 floating

Answer should be B I. e 14 because factorisation of 48 is 2^4*3 so highest power of 2 will be 31 and 3 will be 14 so answer should be 14.

Get the prime factors of 48: 2^4×3^1
find the highest powers of 2 and 3 in 32!
highest power of 2 is 31 in 32!
highest power of 3 is 14 in 32!
now divide highest power of 2 i.e [31/4] = 7
and [14/1] = 14
therefore maximum power of 48 is min(7,15) = 7

Soubhik Das
Jan 30, 2021
48=(2^4) *3. No. of 2's in 32! =31.Now no. of 2^4 in 2^31 is [31/4]=7...we have to determine power of 48 in 32! so first break 48 into prime factors and take the largest factor here it's 2^4.(since 2^4>3)

Ankit Khatoliya
Oct 18, 2020
48= 2^4 *3
highest power of 3 in 32!= 32/3+10/3+3/3 =10+3+1= 14
highest power of 2 in 32!= 32/2+16/2+8/2+4/2+2/2= 16+8+4+2+1=31
highest power of  2^4 in 32!= 7
as 7 is least among 7 and 14, thus 7 will be the highest power

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