Break any number into primes with a factor tree or the division method, and see why you always get the same primes.
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Any number can be written as a product of primes, and in only one way.
Listing all the factors gets long for numbers like 30 and 50, or 28 and 42. It is also easy to miss one.
Prime factorisation makes finding the HCF simpler and more reliable.
Starting differently still ends with the same primes.
Problem. 90 can be split as or . Do both lead to the same primes? (Textbook p. 49)
Spot complete prime factorisations.
Which is the prime factorisation of 90?
Two ways to set out a prime factorisation neatly.
Each circled number is the product of the number on its left and the number below it.
Each time, split a composite number so that at least one factor is prime. Stop when you reach a prime.
The book's two factor trees and their division-method versions.
Problem. Write the prime factorisations of 105 and 30 using the book's figures. (Textbook pp. 49–50)
Fill in the division method for 1200.
Textbook p. 50: find the prime factorisation of 1200 with the division method.
2 | 1200 →
2 | 600 →
2 | 300 →
2 | 150 →
3 | 75 →
5 | 25 →
5 | 5 → 1
So 1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5. Much easier than 1200 = 40 × 30 = 5 × 8 × 5 × 6 = …
Prime factorisations with the division method.