Answer:
2·3
Explanation:
You want the prime factorization of 6, with factors in increasing order.
Six
Your knowledge of multiplication tables tells you that ...
6 = 2·3
Both 2 and 3 are prime numbers, neither of which is a repeated factor. So, neither factor needs an exponent. The prime factorization is ...
6 = 2·3
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Additional comment
The full list of the divisors of 6 is {1, 2, 3, 6}. When we are looking for the prime factorization, we only consider the divisors that are prime, and the values they must be multiplied by.
If we were looking at prime factorization of 12, we would note that 12 has divisors of 1, 2, 3, 4, 6, 12. After we factor out the primes 2 and 3, we see ...
12 = (2·3)·(2)
That is, 2 is a factor repeated twice, so the prime factorization with exponents for 12 is ...
12 = 2²·3
It is helpful to know the first few primes: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...}
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