Question

greatest common factor - item 992215
drag each pair of numbers to show if their greatest common factor (gcf) is less than 3, equal to 3, or greater than 3.
3 and 6 12 and 13 4 and 12 6 and 18 12 and 21 6 and 27
gcf is less than 3.
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gcf is equal to 3.
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gcf is greater than 3.
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Explanation:

Step1: Find GCF of 3 and 6

Factors of 3: \(1, 3\); Factors of 6: \(1, 2, 3, 6\). GCF is \(3\) (equal to 3).

Step2: Find GCF of 12 and 13

12 and 13 are coprime, factors of 12: \(1, 2, 3, 4, 6, 12\); factors of 13: \(1, 13\). GCF is \(1\) (less than 3).

Step3: Find GCF of 4 and 12

Factors of 4: \(1, 2, 4\); factors of 12: \(1, 2, 3, 4, 6, 12\). GCF is \(4\) (greater than 3).

Step4: Find GCF of 6 and 18

Factors of 6: \(1, 2, 3, 6\); factors of 18: \(1, 2, 3, 6, 9, 18\). GCF is \(6\) (greater than 3).

Step5: Find GCF of 12 and 21

Factors of 12: \(1, 2, 3, 4, 6, 12\); factors of 21: \(1, 3, 7, 21\). GCF is \(3\) (equal to 3).

Step6: Find GCF of 6 and 27

Factors of 6: \(1, 2, 3, 6\); factors of 27: \(1, 3, 9, 27\). GCF is \(3\) (equal to 3).

Answer:

• GCF is less than 3: 12 and 13
• GCF is equal to 3: 3 and 6, 12 and 21, 6 and 27
• GCF is greater than 3: 4 and 12, 6 and 18