To find the Greatest Common Factor (GCF) of three numbers, we need to find the largest number that divides evenly into all three of them.
Here is the step-by-step solution for each problem:
1) 8, 14, 12
* Factors of 8: 1,
2, 4, 8
* Factors of 14: 1,
2, 7, 14
* Factors of 12: 1,
2, 3, 4, 6, 12
* The largest factor they share is
2.
2) 12, 24, 14
* Factors of 12: 1,
2, 3, 4, 6, 12
* Factors of 24: 1,
2, 3, 4, 6, 8, 12, 24
* Factors of 14: 1,
2, 7, 14
* The largest factor they share is
2.
3) 15, 20, 5
* Factors of 15: 1, 3,
5, 15
* Factors of 20: 1, 2, 4,
5, 10, 20
* Factors of 5: 1,
5
* Since 5 is one of the numbers, and it divides evenly into 15 and 20, the GCF is
5.
4) 4, 16, 6
* Factors of 4: 1,
2, 4
* Factors of 16: 1,
2, 4, 8, 16
* Factors of 6: 1,
2, 3, 6
* The largest factor they share is
2.
5) 24, 15, 6
* Factors of 24: 1,
3, 2, 4, 6, 8, 12, 24
* Factors of 15: 1,
3, 5, 15
* Factors of 6: 1,
3, 2, 6
* The largest factor they share is
3.
6) 7, 21, 18
* Factors of 7: 1, 7 (7 is prime)
* Factors of 21: 1, 3, 7, 21
* Factors of 18: 1, 2, 3, 6, 9, 18
* The only factor they share is
1.
7) 12, 2, 24
* Factors of 12: 1,
2, 3, 4, 6, 12
* Factors of 2: 1,
2
* Factors of 24: 1,
2, 3, 4, 6, 8, 12, 24
* Since 2 is one of the numbers, and it divides evenly into 12 and 24, the GCF is
2.
8) 20, 10, 25
* Factors of 20: 1, 2, 4, 5, 10, 20
* Factors of 10: 1, 2, 5, 10
* Factors of 25: 1, 5, 25
* The largest factor they share is
5.
9) 3, 18, 9
* Factors of 3: 1,
3
* Factors of 18: 1, 2, 3, 6, 9, 18
* Factors of 9: 1, 3, 9
* Since 3 is one of the numbers, and it divides evenly into 18 and 9, the GCF is
3.
10) 6, 16, 18
* Factors of 6: 1,
2, 3, 6
* Factors of 16: 1,
2, 4, 8, 16
* Factors of 18: 1,
2, 3, 6, 9, 18
* The largest factor they share is
2.
Final Answer:
1) 2
2) 2
3) 5
4) 2
5) 3
6) 1
7) 2
8) 5
9) 3
10) 2
Parent Tip: Review the logic above to help your child master the concept of greatest common factor worksheet 3 digits.
