Answer:
- 28g
- 6cd
Step-by-step explanation:
1. You can factor these to prime factors, then look for common factors:
56g = 2^3 · 7 · g
84gh = 2^2 · 3 · 7 · g · h
Factors that are common to both are 2^2 · 7 · g = 28g.
When a factor is raised to a power, the least power is the common factor:
2^2 and 2^3 have a greatest common factor of 2^2
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2. Same deal.
18cd = 2 · 3^2 · c · d
30cd = 2 · 3 · 5 · c · d
Factors that are common to both are 2 · 3 · c · d = 6cd.
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Comment on GCF of integers
It is helpful to be familiar with multiplication tables and divisibility rules when factoring integers. It can also be helpful to be aware of Euclid's algorithm for finding the GCF of two numbers.
- Divide the larger by the smaller. If the remainder is zero, the smaller is the GCF.
- If the remainder is not zero, replace the larger number by the remainder and repeat from step 1.
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Using this algorithm on 56 and 84, we find ...
84/56 = 1 remainder 28
56/28 = 2 remainder 0, so 28 is the GCF of 56 and 84.
Using this algorithm on 18 and 30, we find ...
30/18 = 1 remainder 12
18/12 = 1 remainder 6
12/6 = 2 remainder 0, so 6 is the GCF of 18 and 30.
