L4 · Greatest Common Factor within 100

Learning goal

“I can find the greatest common factor (GCF) of two numbers within 100: I list both factor lists, circle the factors they SHARE, and choose the greatest one.”

Common factor — a factor that appears in BOTH numbers' factor lists. 3 is a common factor of 12 and 18.

Greatest common factor (GCF) — the biggest of the common factors. For 12 and 18, the GCF is 6. (Also called the greatest common divisor.)

Worked example

Find the GCF of 12 and 18. Step 1 (list): Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Step 2 (share): Which numbers appear in BOTH lists? 1, 2, 3, 6 - these are the common factors. Step 3 (greatest): The greatest of the common factors is 6. The GCF of 12 and 18 is 6. Say it plainly: GCF is a three-step job - list, share, greatest. The answer is never just "a common factor"; it must be the GREATEST one.

Check yourself — explain it

Why isn't the GCF of 12 and 18 equal to 3?

Paired problem — example still visible

Find the GCF of 8 and 20. -> Factors of 8: 1, 2, 4, 8; of 20: 1, 2, 4, 5, 10, 20; common: 1, 2, 4; GCF = 4.

Faded completion — last step is yours

"GCF of 15 and 25: factors of 15 are 1, 3, 5, 15; factors of 25 are 1, 5, 25. Common factors: 1, 5. So the GCF is ___." -> 5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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