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# Prime Factorization and Divisors

Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic.

What is the smallest positive integer divisible by each of 10, 20, and 30?

What is \(a \times b \, ?\)

**Hint:** \(5040 = 7! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7.\)

What is the smallest number that is divisible by 1, 2, 3, 4, 5 and 6?

Which of these statements are true?

I. Even numbers are never divisible by odd numbers.

II. Odd numbers are never divisible by even numbers.

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