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Find the greatest no that divides 42 90 and 182 so as to leave the same remainder in each case

🗓 Dec 10, 2024

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Santos - IIT Delhi 🌐 Tamil Nadu
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:

differences are :

182 - 90 = 92,
182 - 42 = 140,
90 - 42 = 48.

HCF of the differences

HCF of 48 = 2 × 2 × 2 × 2 × 3,
HCF of 92 = 2 × 2 × 23,
HCF of 140 = 2 × 2 × 5 × 7

HCF = 2 × 2 = 4 (Answer)
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Anonymous 🌐 India
Find the greatest number that divides 42, 90 and 182 so as to leave the same remainder
in each case.
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