Prime Factorization

Learn to break down numbers into their prime factors

Prime Factorization

Prime Numbers

A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.

Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Note: 2 is the only even prime number!

Composite Numbers

A composite number is a whole number greater than 1 that has more than two factors.

Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16...

Prime Factorization

Prime factorization means writing a number as a product of prime numbers.

Example: $24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3$

Methods

Factor Tree Method: Break down the number step by step
Division Method: Divide by prime numbers starting from 2

Why It's Useful

Prime factorization helps us:

Find the Greatest Common Factor (GCF)
Find the Least Common Multiple (LCM)
Simplify fractions

📚 Practice Problems

1Problem 1easy

❓ Question:

Find the prime factorization of 18.

💡 Show Solution

Solution:

Using a factor tree: $18 = 2 \times 9$ $9 = 3 \times 3$

So: $18 = 2 \times 3 \times 3 = 2 \times 3^2$

Answer: $18 = 2 \times 3^2$

2Problem 2medium

❓ Question:

Is 37 a prime number or composite number? Explain.

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Solution:

Check if any prime numbers less than 37 divide it evenly:

$37 \div 2 = 18.5$ (not whole)
$37 \div 3 = 12.33...$ (not whole)
$37 \div 5 = 7.4$ (not whole)
We only need to check up to $\sqrt{37} \approx 6$

Since no prime numbers divide 37 evenly, it has no factors other than 1 and 37.

Answer: 37 is a prime number

3Problem 3hard

❓ Question:

Find the prime factorization of 180.

💡 Show Solution

Solution:

Using the division method: $180 \div 2 = 90$ $90 \div 2 = 45$ $45 \div 3 = 15$ $15 \div 3 = 5$ $5 \div 5 = 1$

So: $180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5$

Answer: $180 = 2^2 \times 3^2 \times 5$

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