Question

4) It is known that 3 is the remainder when 99 is divided by a, and 70 is 2 short from being divisible by a. How many positive integers can a be

Answer 1

• 5 integers: {4, 6, 8, 12, 24}

Explanation:

From the given info we have:

• 99 - 3 = 96 is divisible by the number, the number is greater than 3 since the remainder was 3.
• 70 + 2 = 72 is divisible by same number.

Using the above info, find all factors of the two numbers, greater than 3:

• 96 = 4*24 = 6*16 = 8*12 = 12*8 = 16*6 = 24*4 = 32*3 = 48*2
• 72 = 4*18 = 6*12 = 8*9 = 12*6 = 18*4 = 24*3 = 36*2

The common divisors are:

• 4, 6, 8, 12, 24