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To find out what numbers will divide both 69 and 72 exactly, we look at the prime numbers that, when multiplied together, give each of those numbers:

69=23*3

72=3*3*2*2*2

since the divisors of those numbers will be either those primes or some multiples of them (in addition to 1), we look to see what primes they have in common. There is only one, so that number is the only common divisior other than 1. Thus the answer is 3.

Fun fact: Any number, like 7917 for example, is divisible by 3 when the sum of its integers is divisible by 3. (7+9+1+7=24) The same holds true for 9 (7479, 7+4+7+9=27)

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Q: What will go into 69 that will also go into 72?
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