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Mrac [35]
3 years ago
5

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 i

ntegers can a be
Mathematics
1 answer:
katrin2010 [14]3 years ago
6 0

Answer:

  • 5 integers: {4, 6, 8, 12, 24}

Step-by-step explanation:

<u>From the given info we have:</u>

  • 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.

<u>Using the above info, find all factors of the two numbers, greater than 3:</u>

  • 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

<u>The common divisors are:</u>

  • 4, 6, 8, 12, 24
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