1A Factors & Multiples Study Guide

📘 Key Vocabulary

Factor — a number that divides evenly into another number. (factor)

Multiple — the result of multiplying a number by a whole number. (múltiplo)

Prime Number — a number greater than 1 that has only two factors: 1 and itself. (número primo)

Composite Number — a number that has more than two factors. (número compuesto)

Prime Factorization — writing a number as a product of its prime factors. (factorización prima)

GCF (Greatest Common Factor) — the largest factor two or more numbers share. (MCD – Máximo Común Divisor)

LCM (Least Common Multiple) — the smallest multiple two or more numbers share. (MCM – Mínimo Común Múltiplo)

Break a number into two factors, then keep breaking until all factors are prime.

Factor Tree for 12

    12
   /  \
  2    6
      / \
     2   3

12 = 2 × 2 × 3

Factor Tree for 18

    18
   /  \
  2    9
      / \
     3   3

18 = 2 × 3 × 3

Finding GCF of 12 and 18 using factor trees:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
Shared prime factors: 2 × 3 = 6 → GCF = 6

Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common: 1, 2, 4, 8 → GCF = 8

Multiples of 6: 6, 12, 18, 24, 30…
Multiples of 8: 8, 16, 24, 32…
LCM = 24

GCF = the largest factor shared by two or more numbers

LCM = the smallest multiple shared by two or more numbers

Factor vs. Multiple are opposites: Factors go INTO a number (smaller or equal). Multiples come FROM a number (larger or equal).
"Product" is a multi-meaning word: In math it means the answer when you multiply. Outside math it can mean something you buy.
1 is NOT a prime number! Prime numbers must have exactly two factors. The number 1 only has one factor (itself).
GCF is never bigger than the smaller number. LCM is never smaller than the bigger number.

1. Find the GCF of 16 and 24.

2. Find the LCM of 6 and 8.

3. Write the prime factorization of 36. Use × between factors (example: 2×2×3).

4. Is 17 prime or composite? Type "prime" or "composite".