5) The gratest numbers which divides 29,60 and 103 leaving reminder 5,12,7 is ?
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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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