In how many ways can 648 mobiles be distributed equally among the students of a class?
20
The mobiles can be shared equally only if the number of students is a factor of 648, so we count the factors of 648.
Prime factorisation: \(648 = 2^3 \times 3^4\).
Number of factors = \((3 + 1)(4 + 1) = 4 \times 5 = 20\).
So there are 20 ways of distributing the mobiles equally.
Hence, 20.
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Important Questions from Multiples and Factors
Express 486 as a product of powers of prime factors.
Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression \(\frac{p-q-1}{r-s}\) is:
Find the greatest three-digit number which is a multiple of 8.
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
If 2160 = 2 a × 3 b × 5 c , then the value of 3 a × 2 -b × 5 -c will be –
