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Awli
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If the number of different positive factors of (2^y)(3^3) is the same Updated on: 14 Apr 2015, 04:31
Originally posted by Awli on 13 Apr 2015, 09:43.
Last edited by Bunuel on 14 Apr 2015, 04:31, edited 1 time in total.
Edited the question.
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B
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Difficulty:

35% (medium)

Question Stats:

67% (01:11) correct 33% (01:28) wrong based on 202 sessions

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If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

A. 11
B. 12
C. 13
D. 48
E. 51
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B
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Lucky2783
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If the number of different positive factors of (2^y)(3^3) is the same 13 Apr 2015, 10:51
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Awli
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51
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Number of factors of \(N= a^x * b^y\) where 'a' and 'b' are prime factors of N is

(X+1) (y+1)


So 4 (y+1)=52
y=12
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Awli
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If the number of different positive factors of (2^y)(3^3) is the same 13 Apr 2015, 11:28
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Lucky2783
Awli
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51

Number of factors of \(N= a^x * b^y\) where 'a' and 'b' are prime factors of N is

(X+1) (y+1)


So 4 (y+1)=52
y=12
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Why 4 (y+1) ??

Thanks
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If the number of different positive factors of (2^y)(3^3) is the same 13 Apr 2015, 23:38
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Its the number of factor .....
(x+1) (3+1) = 51+1------------------ equation no 1
(x+1)4 = 52
if you solve it will become
y =12

number of factors theory :
N = (a^n )(b^m)
a, b are prime factors of N raised to power n and m .

and number of factors = (n+1)(m+1) -------- this is what use in equation no 1

kudos appreciated . :)
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If the number of different positive factors of (2^y)(3^3) is the same 14 Apr 2015, 04:30
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Awli
If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?

a) 11

b) 12

c) 13

d) 48

e) 51
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Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

According to the above, the number of factors o f (2^y)(3^3) is (y + 1)(3 + 1) = 4y +4 and the number of factors of 2^51 is 51 + 1 = 52. Thus given that 4y +4 = 52 --> y = 12.

Answer: B.

Hope it's clear.
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If the number of different positive factors of (2^y)(3^3) is the same 31 May 2023, 20:24
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