Find the greatest number which divides 38, 47 and 76 leaving remainder 3, 2 and 1 respectively.

Given: 38, 47 and 76 

To find: Here we have to find a number that divides 38, 47 and 76 leaving the remainder 3, 2 and 1 respectively.

Solution:

If we subtract the remainders, then we will get the numbers that are exactly divisible by the unknown number.

38 $-$ 3 = 35

47 $-$ 2 = 45

76 $-$ 1 = 75

The answer will be HCF OF 35, 45 and 75:

75 = 3 $ \times $ 5² 

35 = 5 $ \times $ 7 

45 = 3² $ \times $ 5 

The highest common factor of 75, 35 and 45 is 5.

So, the number that divides 38, 47 and 76 leaving the remainder 3, 2 and 1 respectively is 5.

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Updated on: 10-Oct-2022

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