Question

find the greatest number that can divide 166 and 237 leaving remainders 5 and 7 respectively.

Answer 1

Given number - 166 and 237
Remainder = 5 and 7 respectively
Now,
166 - 5 = 161 = 7 * 23
237 - 7 = 230 = 5 * 2 * 23
H. C. F. = 23
Hence, the number is 23

Answer 2

Concept Introduction:

The quantity that is "leftover" after conducting a calculation is referred to as the remnant in mathematics. The integer that remains after multiplying one number by another one to create an integer quotient is known as the remnant in mathematics.

Given, $166$ and $237$.

remainders $5$ and $7$ respectively.

To find, the greatest number that can divide $166$ and $237$ leave remainders $5$ and $7$ respectively.

Solution:

$166 - 5 = 161 = 7$ ×$23$

$237 - 7 = 230 = 5$$237 - 7 = 230 = 5$ ×$2$ ×$23$

H.C.F = $23$

Final Answer:

The greatest number is $23$

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