Tuesday, December 30, 2014

factors

How many even factors are there for the number 612 x 714 x 87 x 105



Answer:
Expressing  612 x 714 x 87 x 105 in terms of prime factors we have
212 x 312 x 714 x 221 x 25 x 55 = 238 x 312 x 714 x 55
Total number of factors = (38 + 1)(12 + 1)(14 + 1)(5 + 1) = 39x13x15x6 = 45630
Total number of odd factors= (12 + 1)(14 + 1)(5 + 1) = 13 x 15 x 6 = 1170

Total number even factors = 45630 – 1170 = 44460

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