Question

What is the greatest number that will divide 38, 45 and 52 and leaves as remainders 2, 3 and 4 respectively?

Answer 1

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Answer 2

6 is the greatest number that will divide 38, 45 and 52 and leaves as remainders 2, 3 and 4 respectively.

Step-by-step explanation:

Given,

The remainders = 2, 3, and 4 respectively on dividing 38, 45, and 52.

So,

38 - 2 = 36

45 - 3 = 42

52 - 4 = 48

By finding HCF of 36, 42, and 48;

36  = 2 * 2 * 3 * 3

42 = 2 * 3 * 7

48  = 2 * 2 * 2 * 2 * 3

H.C.F. = 2 * 3

= 6

Thus, 6 is the greatest number that will divide 38, 45, and 52 and leaves as remainders 2, 3, and 4 respectively.

Learn more: Greatest Number

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