Question

what is the hcf of (x-y) and (y-x) ? * please help me* ​

Answer 1

Answer:

If the HCF of two numbers, x and y is h , then what would be the HCF of (x+y) and (|x−y|) ?

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CASE 1:

If the two numbers have common factor=1, (co-primes)

Then HCF of x+y and |x-y| will be unpredictable

Examples:

a) Let the two numbers be 7, 9

x+y=16, x-y=2

HCF= 2

b) Let the two numbers be 3,4

x+y=7, |x-y|=1

HCF=1

CASE 2:

If the two numbers have a common factor other than 1 (SAY h)

Then the HCF of x+y and |x-y| will be h itself. (PARDON ME FOR THE EXPLANATION)

Examples:

a) let the two numbers be 4, 6 HCF=2

now x+y=10, x-y=2

HCF of these numbers =2 (Same)

b) let the two numbers be 24, 60 HCF=12

now x+y=84, x-y=36

HCF of these numbers =12 (Same)