Prime factorization — 5th grade math

To find all the prime factors of any number, we can use a factor tree. To start the factorization process, simply write the number as a product (as a multiplication) in any way you like (except 1 × the number). That gives you two "branches". Then factor the numbers you get from that, repeatedly, until you only have primes. At that point, we "pick" the "leaves", or the prime factors, and then write the number's prime factorization.

I show you several examples of this process. Then, I show how it doesn't matter how you START the factoring process, by starting the factorization of 40 in two different ways (either as 2 × 20 or 5 × 8).

Lastly we look at the OPPOSITE process: that of BUILDING numbers from primes. If you pick any primes and multiply them, you get some number... and the primes you picked at first form the unique prime factorization of that number.

The fact is, each number has a unique prime factorization. In other words, each number can be written as a product of primes, and in a unique way. This fact is quite amazing to think about!

See also

Introduction to primes — video lesson

Divisibility rules — video lesson

Math Mammoth Grade 5 curriculum

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