find the greatest common factor of 3 numbers Math Worksheets, Math ... - Free Printable

Let’s solve each set of three numbers to find their Greatest Common Factor (GCF). The GCF is the largest number that divides all three numbers without leaving a remainder.

We’ll go one by one:

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1. 40, 576, 480

First, let’s factor each number or use division to find common factors.

Start with small primes:

- All are even → divisible by 2.
- 40 ÷ 2 = 20; 576 ÷ 2 = 288; 480 ÷ 2 = 240 → still all even → divide by 2 again.
- 20 ÷ 2 = 10; 288 ÷ 2 = 144; 240 ÷ 2 = 120 → still even → divide by 2 again.
- 10 ÷ 2 = 5; 144 ÷ 2 = 72; 120 ÷ 2 = 60 → now 5 is odd, so stop dividing by 2.

So we divided by 2 three times → 2³ = 8.

Now check if 5, 72, and 60 have any common factor?
5 is prime, doesn’t divide 72 or 60 evenly → no more common factors.

→ GCF = 8

Wait — let me double-check: Is there a bigger common factor?

Check 16: 40 ÷ 16 = 2.5 → not whole → so 16 too big.

Check 8: 40÷8=5, 576÷8=72, 480÷8=60 → yes, all work.

Is there a larger one? Try 10: 576 ÷ 10 = 57.6 → no.

Try 4: works, but smaller than 8.

So GCF = 8

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2. 9, 72, 36

All divisible by 9?

9 ÷ 9 = 1
72 ÷ 9 = 8
36 ÷ 9 = 4 → yes!

Is there a bigger one? Next multiple would be 18: 9 ÷ 18 = 0.5 → no.

So GCF = 9

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3. 48, 32, 24

All even → divide by 2: 24, 16, 12
Again by 2: 12, 8, 6
Again by 2: 6, 4, 3 → now 3 is odd, others even → stop.

Divided by 2 three times → 8.

Check if 6, 4, 3 have common factor? No.

But wait — try 4: 48÷4=12, 32÷4=8, 24÷4=6 → works.

Try 8: 48÷8=6, 32÷8=4, 24÷8=3 → also works! And 8 > 4.

Can we go higher? 16: 24÷16=1.5 → no.

So GCF = 8

Wait — earlier I thought 8, but let me confirm:

Factors of 24: 1,2,3,4,6,8,12,24
Factors of 32: 1,2,4,8,16,32
Factors of 48: 1,2,3,4,6,8,12,16,24,48
Common: 1,2,4,8 → greatest is 8 → correct.

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4. 8, 100, 24

All even → divide by 2: 4, 50, 12
Again by 2: 2, 25, 6 → now 25 is odd, others even → stop.

Divided by 2 twice → 4.

Check if 2, 25, 6 have common factor? 25 is 5×5, 2 and 6 don’t share 5 → no.

Try 4: 8÷4=2, 100÷4=25, 24÷4=6 → yes.

Try 8: 100÷8=12.5 → no.

So GCF = 4

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5. 4, 48, 80

All divisible by 4?

4÷4=1, 48÷4=12, 80÷4=20 → yes.

Any bigger? 8: 4÷8=0.5 → no.

So GCF = 4

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6. 120, 210, 1050

Let’s find GCF step by step.

First, note all end in 0 → divisible by 10.

120÷10=12, 210÷10=21, 1050÷10=105

Now find GCF of 12, 21, 105.

Factors:

12: 1,2,3,4,6,12
21: 1,3,7,21
105: 1,3,5,7,15,21,35,105

Common factor: 3

So total GCF = 10 × 3 = 30

Check: 120÷30=4, 210÷30=7, 1050÷30=35 → all whole numbers → correct.

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7. 12, 60, 120

All divisible by 12?

12÷12=1, 60÷12=5, 120÷12=10 → yes.

Bigger? 24: 12÷24=0.5 → no.

So GCF = 12

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8. 18, 120, 225

Find common factors.

First, check divisibility by 3:

18÷3=6, 120÷3=40, 225÷3=75 → yes.

Again by 3? 6÷3=2, 40÷3≈13.33 → no.

So only one 3.

Check for other common factors? 2: 225 is odd → no.

5: 18 not divisible by 5 → no.

So GCF = 3

Wait — let me check again.

List factors:

18: 1,2,3,6,9,18
120: 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
225: 1,3,5,9,15,25,45,75,225

Common factors: 1, 3 → greatest is 3 → correct.

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9. 96, 192, 256

Note: 192 = 2×96 → so GCF of 96 and 192 is 96.

Now find GCF of 96 and 256.

Factor them:

96 = 32 × 3 = 2⁵ × 3
256 = 2⁸

Common prime factor: 2⁵ = 32

So GCF = 32

Check: 96÷32=3, 192÷32=6, 256÷32=8 → all whole → correct.

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10. 60, 96, 60

Two 60s and one 96.

GCF of 60 and 96.

Factor:

60 = 2² × 3 × 5
96 = 2⁵ × 3

Common: 2² × 3 = 4 × 3 = 12

So GCF = 12

Check: 60÷12=5, 96÷12=8 → yes.

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Now compile all answers:

1. 40, 576, 480 → 8
2. 9, 72, 36 → 9
3. 48, 32, 24 → 8
4. 8, 100, 24 → 4
5. 4, 48, 80 → 4
6. 120, 210, 1050 → 30
7. 12, 60, 120 → 12
8. 18, 120, 225 → 3
9. 96, 192, 256 → 32
10. 60, 96, 60 → 12

Final Answer:
8, 9, 8, 4, 4, 30, 12, 3, 32, 12