Find the total number of prime factors of the number \(5^{8} \\times 6^{7} \\times 11^{4}\).
26
Factorise every base into primes: \(5^{8}\) contributes eight 5s; \(6^{7} = (2 \\times 3)^{7} = 2^{7} \\times 3^{7}\) contributes seven 2s and seven 3s; \(11^{4}\) contributes four 11s.
The complete prime factorisation is \(2^{7} \\times 3^{7} \\times 5^{8} \\times 11^{4}\).
The total number of prime factors (counted with multiplicity) is \(7 + 7 + 8 + 4 = 26\).
Hence, the total number of prime factors is 26.
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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 smallest prime number is:
The sum of three consecutive multiples of 7 is 840. The smallest of these multiples is:
