Find the largest positive integer that divides 125,162 and 259 leaving remainder 5,6and 7 respectively
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answer is 12 by first subtract them and then HCF
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Answer:
Largest positive integer = 12
Step-by-step explanation:
To find the largest positive integer, let us take the largest positive divisor to be x.
When, 125 ÷ x, Remainder = 5.
Hence, (125 - 5) i.e. 120 is divisible by x.
When, 162 ÷ x, Remainder = 6.
Hence, (162 - 6) i.e. 156 is divisible by x.
When, 259 ÷ x, Remainder = 7.
Hence, (259 - 7) i.e. 252 is divisible by x.
∴x= H.C.F of 120, 156, 252.
By Euclid Division Method,
Thus, x= H.C.F of 120, 156, 252 = 12.
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