Pre-Algebra
Numbers and operations
Prime factorisation
20 practice questions
0 video lessons
Theory + worked examples
Prime Factorization
Texas Pre-Algebra (TEKS) • Standard 6.7(A) • Numbers & Operations
Prime Factorization is a topic in Numbers & Operations in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.7(A), which requires students to write a whole number as a product of its prime factors.
Prime factorization writes a whole number as a product of prime numbers, often found with a factor tree.
Theory
Prime factorization writes a number as a product of prime numbers — numbers whose only factors are \(1\) and themselves.
A factor tree breaks the number down step by step.
A factor tree for \(60\).
What prime factorization is.
Example:
\[60=2^2\cdot3\cdot5\]
Every whole number has one prime factorization.
How to prime factorize
- Split into any two factors.
- Keep splitting composite factors.
- Stop when every branch is prime.
- Write the product using exponents.
Example 1 — Small number
Factor \(12\) into primes.
Solution
\(12=4\cdot3=2^2\cdot3\).
| \(12\) | \(=\) | \(2^2\cdot3\) |
Example 2 — Larger
Factor \(45\) into primes.
Solution
\(45=9\cdot5=3^2\cdot5\).
| \(45\) | \(=\) | \(3^2\cdot5\) |
Example 3 — Is it prime?
Is \(17\) prime?
Solution
Its only factors are \(1\) and \(17\) — yes.
Example 4 — Use it
Factor \(100\).
Solution
\(100=2^2\cdot5^2\).
| \(100\) | \(=\) | \(2^2\cdot5^2\) |
Common pitfalls
\(1\) is not prime.
Keep factoring until all factors are prime.
Use exponents for repeated primes.
Frequently asked questions
What is prime factorization?
Writing a number as a product of primes.
What is a prime number?
A number with exactly two factors, \(1\) and itself.
Is 1 prime?
No.
Factor \(60\).
\(2^2\cdot3\cdot5\).
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