Greatest common factor
2) 49 and 84
GCF______
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Greatest common factor
2) 49 and 84
GCF______
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Answer:
7
Step-by-step explanation:
Given: GCF (x, 84) = 7 and LCM (x, 84) = 588
∵ GCF × LCM = 84 × (x)
⇒ x = (GCF × LCM)/84
⇒ x = (7 × 588)/84
⇒ x = 49
Therefore, the other number is 49.
Example 2: Find the greatest number that divides 49 and 84 exactly.
Solution:
The greatest number that divides 49 and 84 exactly is their greatest common factor, i.e. GCF of 49 and 84.
⇒ Factors of 49 and 84:
Factors of 49 = 1, 7, 49
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the GCF of 49 and 84 is 7.
Example 3: Find the GCF of 49 and 84, if their LCM is 588.
Solution:
∵ LCM × GCF = 49 × 84
⇒ GCF(49, 84) = (49 × 84)/588 = 7
Therefore, the greatest common factor of 49 and 84 is 7.