GCF, LCM, and Prime Factorization Flashcards

Grade 6 · Math · Flashcards

Essential vocabulary and methods for GCF, LCM, and prime factorization in Grade 6.

Flashcards

Prime number: A whole number > 1 with exactly two factors: 1 and itself
Composite number: A whole number > 1 with more than two factors
Is 1 prime?: No — 1 has only one factor (itself), so it is neither prime nor composite
Prime factorization: Expressing a number as a product of primes only — e.g. 28 = 2² × 7
Factor tree: A method: repeatedly factor until all branches end in prime numbers
GCF: Greatest Common Factor — the largest number that divides two numbers evenly
Finding GCF with prime factorization: Multiply shared primes using the LOWEST exponent found in either number
LCM: Least Common Multiple — the smallest number divisible by two given numbers
Finding LCM with prime factorization: Multiply ALL primes from both numbers using the HIGHEST exponent
GCF of prime numbers: Always 1 — different primes share no factors other than 1
GCF use case: Simplifying fractions: divide numerator and denominator by their GCF
LCM use case: Finding a common denominator when adding or subtracting fractions
GCF(12, 18) = ?: 6 — because 12=2²×3 and 18=2×3², shared: 2¹×3¹=6
LCM(4, 6) = ?: 12 — because 4=2² and 6=2×3, take highest: 2²×3=12