Greatest Common Factor (GCF) for Kids: 3 Easy Methods

The greatest common factor (GCF) of two numbers is the biggest number that divides into both of them with nothing left over. The GCF of 12 and 18 is 6, because 6 goes into 12 two times and into 18 three times, and no bigger number does that.

If your students already know their multiplication facts and factor pairs, they're ready for GCF. It comes up when simplifying fractions, splitting things into equal groups, and later in algebra. Our 4th grade factoring worksheets build those skills step by step, and below you'll find 3 methods, 10 worked examples with answers and the mistakes to watch for.

What Does GCF Mean?

Break the name into its three words and it explains itself:

• Factor: a number that divides into another number evenly. The factors of 12 are 1, 2, 3, 4, 6 and 12.
• Common: shared by both numbers.
• Greatest: the biggest one.

So the GCF is the biggest factor two numbers share. You'll sometimes see it called the greatest common divisor (GCD) or the highest common factor (HCF). Same idea, different name.

Picture 12 cookies and 18 apples split into identical snack plates with nothing left over. The GCF tells you the most plates you can make: 6 plates, each with 2 cookies and 3 apples.

Method 1: List the Factors

This is the best starting method because students can see every step. It works well for numbers up to about 50.

Example: Find the GCF of 12 and 18.

1. List the factors of 12: 1, 2, 3, 4, 6, 12
2. List the factors of 18: 1, 2, 3, 6, 9, 18
3. Circle the factors in both lists: 1, 2, 3, 6
4. Pick the biggest: 6

Quick tip: have students find factors in pairs so they don't miss any. For 18: 1 x 18, 2 x 9, 3 x 6. When the pairs start repeating, they're done.

Method 2: Factor Trees

A factor tree breaks a number down into prime numbers (numbers whose only factors are 1 and themselves, like 2, 3, 5 and 7). It's faster than listing when the numbers get bigger.

Example: Find the GCF of 24 and 36.

1. Split 24 into any factor pair: 24 = 4 x 6. Keep splitting until every branch ends in a prime: 4 = 2 x 2 and 6 = 2 x 3. So 24 = 2 x 2 x 2 x 3.
2. Do the same for 36: 36 = 6 x 6, and each 6 = 2 x 3. So 36 = 2 x 2 x 3 x 3.
3. Line them up and find the primes they share:
   • 24: 2 x 2 x 2 x 3
   • 36: 2 x 2 x 3 x 3
4. The shared primes are 2, 2 and 3. Multiply them: 2 x 2 x 3 = 12.

Check it: 24 ÷ 12 = 2 and 36 ÷ 12 = 3. It works.

Our prime factor trees worksheets give students practice with step 1 before they use it for GCF.

Method 3: The Ladder (Cake) Method

The ladder method (some teachers call it the cake method because the finished work looks like a stacked cake) divides both numbers at the same time. Honestly, this is the one many students end up liking most, because it's quick and tidy.

Example: Find the GCF of 48 and 60.

Write both numbers side by side. Divide both by any prime that goes into both, and write the answers below. Keep going until no number except 1 divides both.

Divide by	First number	Second number
	48	60
2	24	30
2	12	15
3	4	5

4 and 5 share no factor except 1, so stop. Multiply the numbers down the left side: 2 x 2 x 3 = 12.

Check it: 48 ÷ 12 = 4 and 60 ÷ 12 = 5, the same numbers left at the bottom of the ladder.

10 GCF Examples With Answers

Cover the answers and have students try each one first.

#	Numbers	Work	GCF
1	8 and 12	8: 1, 2, 4, 8 / 12: 1, 2, 3, 4, 6, 12	4
2	15 and 25	15: 1, 3, 5, 15 / 25: 1, 5, 25	5
3	6 and 24	6 divides evenly into 24	6
4	16 and 40	16: 1, 2, 4, 8, 16 / 40: 1, 2, 4, 5, 8, 10, 20, 40	8
5	14 and 35	14: 1, 2, 7, 14 / 35: 1, 5, 7, 35	7
6	7 and 10	7: 1, 7 / 10: 1, 2, 5, 10	1
7	30 and 45	30: 1, 2, 3, 5, 6, 10, 15, 30 / 45: 1, 3, 5, 9, 15, 45	15
8	36 and 54	36 = 2 x 2 x 3 x 3 / 54 = 2 x 3 x 3 x 3 / shared: 2 x 3 x 3	18
9	42 and 56	42 = 2 x 3 x 7 / 56 = 2 x 2 x 2 x 7 / shared: 2 x 7	14
10	18, 27 and 45	18 = 2 x 3 x 3 / 27 = 3 x 3 x 3 / 45 = 3 x 3 x 5 / shared: 3 x 3	9

Two shortcuts hide in that table. Example 3: when the smaller number divides evenly into the bigger one, the smaller number IS the GCF. Example 6: when two numbers share nothing but 1, the GCF is 1.

Bonus word problem: Ms. Rivera has 24 pencils and 36 erasers. She wants to make identical supply kits with nothing left over. What's the greatest number of kits she can make? The GCF of 24 and 36 is 12, so she can make 12 kits, each with 2 pencils and 3 erasers.

How to Teach GCF in Class

Here's the order that works for most classes:

1. Review factor pairs first. If students can't list the factors of 24 quickly, GCF will feel like a guessing game. A few days of factor pair practice pays off.
2. Start with real objects. Hand out counters in two colors (say 8 red and 12 blue). Ask students to make identical groups with nothing left over. They'll find 4 groups is the most, and that's the GCF of 8 and 12.
3. Teach listing before trees. Listing shows WHY the answer works. Trees and ladders are shortcuts, and shortcuts make more sense once students understand the long way.
4. Use word problems early. Equal groups, kits and rows give GCF a purpose.

GCF vs LCM

Your students meet these two together and mix them up constantly, so it helps to put them side by side.

	GCF	LCM
Stands for	Greatest common factor	Least common multiple
Question it answers	What's the biggest number that divides into both?	What's the smallest number both divide into?
Size	Same size or smaller than the smaller number	Same size or bigger than the bigger number
12 and 18	6	36
Typical word problem	Splitting into equal groups	When two schedules line up again

Here's a fun fact for 5th graders: for any two numbers, GCF x LCM = the two numbers multiplied together. For 12 and 18: 6 x 36 = 216, and 12 x 18 = 216. Practice the LCM side with our least common multiple worksheets.

Common GCF Mistakes

Finding A common factor, not the GREATEST. A student sees 2 in both lists and stops. Circle every shared factor, then pick the biggest.

Missing factors. Skipping 6 when listing the factors of 30 changes the whole answer. Finding factors in pairs (1 x 30, 2 x 15, 3 x 10, 5 x 6) fixes this.

Multiplying all the primes. With factor trees, some students multiply every prime from both trees. That gives a huge number that isn't a factor of either. Only the SHARED primes count.

Mixing up GCF and LCM. Quick sense check: the GCF can never be bigger than the smaller number. If a student says the GCF of 8 and 12 is 24, that's the LCM.

Practice GCF With Worksheets

GCF clicks with repetition. Our 4th grade factoring worksheets cover finding factors, prime factor trees, divisibility rules and a GCF practice page, all in one place.

For students ready for bigger numbers, the 5th grade factoring worksheets include GCF of two numbers up to 100 and up to 500, plus LCM and prime factorization.

FAQ

What is the greatest common factor in simple words? The greatest common factor is the biggest number that divides evenly into two or more numbers. For 12 and 18, the numbers that divide into both are 1, 2, 3 and 6. The biggest one is 6, so the GCF is 6.

How do you find the GCF step by step? List all the factors of each number, circle the factors they have in common, then pick the biggest one. For 8 and 12: factors of 8 are 1, 2, 4, 8 and factors of 12 are 1, 2, 3, 4, 6, 12. The common factors are 1, 2 and 4, so the GCF is 4.

What is the GCF of 24 and 36? The GCF of 24 and 36 is 12. Using a factor tree, 24 = 2 x 2 x 2 x 3 and 36 = 2 x 2 x 3 x 3. They share 2 x 2 x 3, which equals 12.

What is the difference between GCF and LCM? The GCF is the biggest number that divides into both numbers, so it is always the same size or smaller than the smaller number. The LCM (least common multiple) is the smallest number both numbers divide into, so it is always the same size or bigger than the bigger number. For 12 and 18, the GCF is 6 and the LCM is 36.

Can the GCF be 1? Yes. When two numbers share no factor except 1, their GCF is 1. For example, 7 and 10 have a GCF of 1. Numbers like these are called relatively prime.

Keep Reading

• Fourth Grade Math: Skills, Strategies, and Practice
• Fifth Grade Math: Preparing for Middle School Success

GCF looks like a lot of steps at first. But once students see it as "the biggest equal groups I can make," the methods start to feel like tools instead of rules. Start with cookies and counters, and the numbers will follow 😊