Prime Factorization
Every integer above 1 is a unique product of primes.
Key idea
Every integer above 1 is a unique product of primes.
In depth
Every whole number above 1 can be written as a product of primes in exactly one way (apart from order). A factor tree breaks a number down until only primes remain. This uniqueness underpins GCD and LCM.
Worked example
60 = 6 × 10 = (2×3)×(2×5) = 2² × 3 × 5.
Formula
Real-world uses
- Simplifying fractions and roots
- Finding the lowest common denominator
- Cryptographic key work
Common mistake
Stopping while a composite factor remains in the tree.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Prime Factorization?
Every integer above 1 is a unique product of primes. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Prime Factorization?
The key formula is 60 = 2² × 3 × 5.
Where is Prime Factorization used in real life?
Real-world examples: Simplifying fractions and roots; Finding the lowest common denominator; Cryptographic key work.
What should I learn before Prime Factorization?
Make sure you are comfortable with Composite Numbers, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Prime Factorization?
Stopping while a composite factor remains in the tree.
How can I practise Prime Factorization?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Prime Factorization?
Move on to Greatest Common Divisor next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.