Greatest number dividing three numbers leaving the same remainder: HCF of their differences

The same question, asked 2 times: CDS 1 2020*, CDS 1 2026. Every wording below, oldest first.

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Question 1
CDS 1 2020
16 $A number divides 12288, 28200 and 44333 so as to leave the same remainder in each case. What is that number ?$
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Question 2
CDS 1 2026
24 $Let N be the greatest number that will divide 600, 631 and 724, leaving the same remainder. What is the value of N ?$
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