1
Question
The largest number which divides 972 and 2016 leaving remainder 15 in each case, is
The largest number which divides 972 and 2016 leaving remainder 15 in each case, is
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Solution
The correct option is B 87
The greatest number which divides 972 and leaves the remainder as 15, will be 972 – 15 = 957.
The factors of 957 are 3 × 11 × 29.
Now consider 2016,
The greatest number which divides 2016 and leaves the remainder as 15, will be 2016 – 15 = 2001.
The factors of 2001 are 3 × 23 × 29.
To find the greatest number that divides the two numbers, we will find the Highest Common Factor.
957 = 3 × 11 × 29
2001 = 3 × 23 × 29
∴ HCF of 957, 2001 is 3 × 29 = 87
Thus, the greatest number that divides 972 and 2016 by leaving 15 as a remainder is 87.
Hence, the correct answer is option (b).
The greatest number which divides 972 and leaves the remainder as 15, will be 972 – 15 = 957.
The factors of 957 are 3 × 11 × 29.
Now consider 2016,
The greatest number which divides 2016 and leaves the remainder as 15, will be 2016 – 15 = 2001.
The factors of 2001 are 3 × 23 × 29.
To find the greatest number that divides the two numbers, we will find the Highest Common Factor.
957 = 3 × 11 × 29
2001 = 3 × 23 × 29
∴ HCF of 957, 2001 is 3 × 29 = 87
Thus, the greatest number that divides 972 and 2016 by leaving 15 as a remainder is 87.
Hence, the correct answer is option (b).
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