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ABC D. The hcf and lcm of two numbers are 32 and 192 respectively. If the square of one of the numbers is a perfect cube, find the numbers. Please help.
2 Answers By Expert Tutors
Andrew M. answered • 05/05/17
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
the numbers must be a multiple of 32
32, 64, 96, 128, 160, 192
The square of one of the numbers
multiples of 32: 32, 64, 96, 128, 160, 192
multiples of 64: 64, 128, 192
the lowest common multiple of
Greatest common factor of
Your numbers are 64 and 96
In this method divide the largest number by the smallest number of the given numbers until the remainder is zero. The last divisor will be the HCF of given numbers.
Divide the largest by the smallest:
192/32 = 6 Remainder 0
The Remainder is already 0, so the HCF is 32 (the last divisor).
PRIME FACTORIZATION METHOD
Given natural numbers are written as the product of prime factors. To obtain highest common factor multiply all the common prime factors with the lowest degree (power).
Write as product of prime factors:
32 = 2*2*2*2*2 = 25
192 = 2*2*2*2*2*2*3 = 26*31
Lowest common degree of 2 is 5 and the degree (exponent) for 3 is zero.
The HCF is 25*30 = 25*1 = 32.