Is 39 a prime or composite Explain how you know?

Answer 1

composite

3 goes into 3 or 30

3 goes into 9

so 3 goes into 39

13 + 13 + 13 = 39 = 3 x 13

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Applying a divisibility test:

To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3.

As the test can be repeated on the sum, repeat the summing until a single digit remains; only if this number is one of {3, 6, 9} is the original number divisible by 3.

For 39 this gives:

39 → 3 + 9 = 12

12 → 1 + 2 = 3

3 is one of {3, 6,9} so 39 is divisible by 3.

As 39 is divisible by 3 (that is 3 is a factor of 39 that is less than 39) and 3 is greater than 1 then 39 is a composite number.