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01 Feb 2026, 23:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
34% (01:45) correct
66%
(02:04)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
‘W’ is the smallest positive integer that has 12 factors. What is the remainder when W is divided by 11 ?
A. 2
B. 5
C. 6
D. 8
E. 9
A. 2
B. 5
C. 6
D. 8
E. 9
02 Feb 2026, 05:56
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Given: W is the smallest positive integer that has 12 factors
We know: The number of factors of N = 2^a * 3^b * 5^c = (a+1)(b+1)(c+1)
Since 12 = 2*2*3, we can express N as 2^a * 3^b * 5^c.
Thus, (a+1)(b+1)(c+1) = 12
So, a = 2, b = 1 and c = 1
Now, since we require W to be the smallest positive ingeter, we would assign the highest power, i.e., 2 to the smallest prime, i.e., 2.
W = 2^2 * 3 * 5 = 4 * 3 * 5 = 60
Remainder when W is divided by 11 = 5
Hence, the correct answer is Option B - 5
Hope this helps!
We know: The number of factors of N = 2^a * 3^b * 5^c = (a+1)(b+1)(c+1)
Since 12 = 2*2*3, we can express N as 2^a * 3^b * 5^c.
Thus, (a+1)(b+1)(c+1) = 12
So, a = 2, b = 1 and c = 1
Now, since we require W to be the smallest positive ingeter, we would assign the highest power, i.e., 2 to the smallest prime, i.e., 2.
W = 2^2 * 3 * 5 = 4 * 3 * 5 = 60
Remainder when W is divided by 11 = 5
Hence, the correct answer is Option B - 5
Hope this helps!
07 Feb 2026, 02:15
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ExpertsGlobal5
Video explanation:
