Question

the HCF of two numbers are 432 and 72 respectively,if one of the numbers is 216,what is the other​

Answer 1

Answer:

First, I will find the Prime Factorization for each of the three numbers:

2*2*2*2*3*3 [Prime Factorization of 144]

2*2*2* 3*3*3 [Prime Factorization of 216]

2*2*2*2*3*3*3 [Prime Factorization of 432 (LCM)]

2*2*2* 3*3 [Prime Factorization of 72(HCF)

From this configuration, given that the Prime Factorization of the LCM must have factors that are in one or the other or both of the two numbers and the HCF must have factors that are in both numbers. Therefore, the missing number must have four 2's and two 3's.

2*2*2*2*3*3=144

Answer: 144 is the other number.

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