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The prime factors of 105 can only be prime numbers less than the square root of 105.

The greatest prime less than the square root of 105 is 7, so the only numbers that need to be considered as possible prime factors of 105 are 2, 3, 5, and 7.

2 cannot be one of its prime factors because 105 is an odd number.

Divide 105 by the next larger possible prime, 3, and the quotient is 35, proving that 3 is a prime factor of 105. 35 cannot be divided by 3, but 5 goes into 35 leaving a quotient of 7.

The prime factorization of 105 is 3 x 5 x 7.

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