What is the greatest number that will divide 99, 123 and 183 leaving the same remainder in each case?
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Answered by
8
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Answer is correct! Nicely done:)
Answered by
5
Answer:
12
Step-by-step explanation:
Note: Look at the differences between the given numbers.
∴ HCF of (123 - 99), (183 - 123), (183 - 99)
= 24, 60, 84
So, we have the set of numbers{24,60,84}, and we want to know the biggest numbers that divides all these numbers.
Prime factorization of 24 = 2³ * 3
Prime factorization of 60 = 2² * 3 * 5
Prime factorization of 84 = 2² * 3 * 7
HCF(24,60,84) = 2² * 3
= 12.
Therefore, the greatest number is 12.
Hope it helps!
Thank you Sir!
Answer is correct. But why does this method work?
Sir, In this question it is said that the remainder in each case is same. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number.
yeah.. got it!!
Thanks again:))
its ok sir!
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