7. find the greatest number which divides 29, 60 and 103 leaving remainders 5, 12 and 7 respectively?
Answers
The greatest number which divides 29, 60 and 103 leaving remainders 5, 12 and 7 respectively is 24.
Step-by-step explanation:
It is given that,
The dividends 29, 60 and 103, when divided by the required greatest number, leaves remainders 5, 12 and 7 respectively.
(1). First, we will have to subtract the remainders from their respective dividends i.e.,
29 - 5 = 24
60 - 12 = 48
103 - 7 = 96
(2). Now, to find the greatest number, we will calculate the H.C.F. of the three numbers so received by the above subtraction i.e.,
24 = 2 × 2 × 2 × 3
48 = 2 × 2 × 2 × 2 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
∴ H.C.F. of 24, 48 & 96 = 2³ × 3 = 24
Thus, the required greatest number is 24.
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Answer:
24
Step-by-step explanation:
First we have find the difference of the numbers with the given remainders after that we have find the hcf of the numbers which have been subtracted and after that you shall get the ans