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प्रश्न
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.
विकल्प
13
65
875
1750
उत्तर
The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is 13.
Explanation:
We have to find the largest number which divides 70 and 125
Leaving remainders 5 and 8
This can be also written as,
To find the largest number which exactly divides (70 – 5) and (125 – 8)
The largest number that divides 65 and 117 is also the Highest Common Factor of 65 and 117
Therefore, the required number is the HCF of 65 and 117
Factors of 65 = 1, 5, 13, 65
Factors of 117 = 1, 3, 9, 13, 39, 117
Common Factors = 1, 13
Highest Common factor (HCF) = 13
i.e., The largest number which divides 70 and 125
Leaving remainders 5 and 8, respectively = 13
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