I think that might be the other way around. 2 and 3 are prime numbers that go into 30.
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Firstly, we find that 2 * 3 = 6. Dividing 30 by 6, (ensuring that 6 goes in), we have 5. Since 5 is prime, 5 must be the missing prime factor.
Just once with a remainder of 7.
8 is not a prime factor of 30. The prime factorization of 30 is 2x3x5.
It is: 13+17 = 30