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Find the greatest number that will divide 517 and 815 leaving the reminders 1 and 3 respectively
Given :
The given numbers are 517 and 815 which leaves the remainders 1 and 3 respectively when we divide by a number.
To do :
We have to find the number.
Solution :
Let the number be 'x'.
When we divide 517 and 815 by x the remainder is 1 and 3.
$517 - 1 = 516$
$815 - 3 = 812$
Now, when we divide 516 and 812 by x the remainder will be 0.
Therefore, x is the HCF of 516 and 812.
Factors of $516 =2 \times 2\times 3 \times 43 = 2^2 \times 3 \times 43$
Factors of 812 $= 2 \times 2 \times 7 \times 29 = 2^2 \times 7 \times 29$
$HCF = Common prime factors with lowest powers$
Therefore, HCF of 516 and 812 is $2^2 = 4$
Therefore, the greatest number will divide 517 and 815 leaving reminders 1 and 3 respectively is 4.
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