Choose the correct answer from the given four options in the foll… - Vidyadip

MCQ

Choose the correct answer from the given four options in the following questions:The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is:

✓
13.
B
65.
C
875.
D
1750.

✓

Answer

Correct option: A.

13.

Since, 5 and 8 are the remainders of 70 and 125, respectively. Thus, after subtracting these remainders from the numbers, we have the numbers 65 = (70 - 5), 117 = (125 - 8), which is divisible by the required number.

Now, required number = HCF of 65, 117 [for the largest number]

117 = 65 × 1 + 52 [$\because$ dividend = divisor × quotient + remainder]

65 = 52 × 1 + 13

52 = 13 × 4 + 0

$\therefore$ HCF = 13

Hence, 13 is the largest number which divides 70 and 125, leaving remainders 5 and 8.

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