Factors, Multiples, and Primes

Factors and Multiples

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
• Multiples of 6: 6, 12, 18, 24, 30, ...

Prime Numbers

Primes have exactly two factors. First primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31...

1 is NOT prime. 2 is the only even prime.

Prime Factorization

$60 = 2^2 \times 3 \times 5$. Use a factor tree.

GCF (Greatest Common Factor)

Multiply common prime factors (lowest powers).

$\text{GCF}(36, 48) = 2^2 \times 3 = 12$.

LCM (Least Common Multiple)

Multiply all prime factors (highest powers).

$\text{LCM}(36, 48) = 2^4 \times 3^2 = 144$.

Divisibility Rules

• By 2: even number. By 3: digit sum divisible by 3. By 5: ends in 0 or 5.
• By 4: last two digits divisible by 4. By 6: divisible by both 2 and 3.