In general when you are asked to handle factors of big numbers, or to think about the properties of really large numbers, it's a good idea to break numbers into their prime factors.
270,000,000 = 27 * 10^7 = 3^3 * 2^7 * 5^7
a, b and c are the exponents of 2, 3 and 5 respectively, so a=7, b=3, c=7.
a*b*c = 7*3*7 = 147
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Integer properties - Any tips to solve this one quickly
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