Find the greatest number that will divide 65, 81,145 leaving the same reaminder in each case
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Find the HCF (GCD) of the difference of given numbers. Its mentioned that we have to find a number which divides the given number to leave same remainder. (exact remainder value is not given)
145 - 65 =80
145 - 81 = 64
81 - 65 =16
Now find the HCF of 80,64,16
80 = 16*5 = 2*2*2*2*5
64=2*2*2*2*2*2
16=2*2*2*2
So HCF is 16.
16 is the greatest number that divides 65,81,145 to leave same remainder.
Concept:
Dividend = Quotient* Divisor + Remainder
Dividend is given, the remainder has to be the same for all dividends, hence divisor is the hcf. From the above equation, we can see that if we subtract our dividends , we get such a number that is exactly divisible by 'divisor'. (since remainders are same, they cancel out on subtraction)
Hope this helps
145 - 65 =80
145 - 81 = 64
81 - 65 =16
Now find the HCF of 80,64,16
80 = 16*5 = 2*2*2*2*5
64=2*2*2*2*2*2
16=2*2*2*2
So HCF is 16.
16 is the greatest number that divides 65,81,145 to leave same remainder.
Concept:
Dividend = Quotient* Divisor + Remainder
Dividend is given, the remainder has to be the same for all dividends, hence divisor is the hcf. From the above equation, we can see that if we subtract our dividends , we get such a number that is exactly divisible by 'divisor'. (since remainders are same, they cancel out on subtraction)
Hope this helps
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