Number Theory I Junior Math Circles - University Of Waterloo Faculty Of Mathematics Worksheet With Answers Page 5
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1
2
3
4
5
6
75
Is 10 prime? No, so we have to prime factor 10.
What is a pair of factors of 10? A pair is 2 and 5.
Both 2 and 5 are prime, so we are done this part.
270
10
27
2
5
Is 27 prime? No, so we have to prime factor it.
What is a pair of factors? One pair is 3 and 9.
The number 3 is prime, but 9 has factors 3 and 3.
270
10
27
9
2
5
3
3
3
We have decomposed 270 into all prime numbers, so now we can write it as a product
of these primes.
270 = 2
3
3
3
5
Note: Prime factorizations are unique. Every number has only one prime factoriza-
tion, and no two numbers have the same prime factorization.
Exercise 5 Find the prime factorization of 2520 using a factor tree.
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