What is the greatest common factor of the following numbers?

Question

29 & 58

18 & 35

90 & 480

80 & 45

700 & 200

17 & 85

24 & 84 & 168

55 & 105

252 & 126

5p & 20p squared

28a & 49ab

8b & 5c

6a squared & 18b squared

88s squared t & 40st squared

42a squared b & 60ab squared

Answer 1

29 & 58 GCF 29
18 and 35 GCF 1
90 and 480 GCF 30
80 and 45 GCF 5
700 and 200 GCF 100
17 and 85 GCF 17
24, 84 and 168 GCF 12
55 and 105 GCF 5
252 and 126 GCF 126
5p
7a
1
6
8s
6a

Good luck

Answer 2

To find the GCF, you need to break down each pair into its prime factors first of all.

For example, 90 and 480
90 = 2 * 3 * 3 * 5
480 = 2 * 2 * 2 * 2 * 2 * 3 * 5

Now for each prime factor (2, 3, 5, 7, 11, 13, etc.), see how many times it appears in each of your numbers and take the LOWEST number of these:

2 -- appears once in 90, 5 times in 480, so take one 2
3 -- appears twice in 90, once in 480, so take one 3
5 -- appears once in 90, once in 480, so take one 5

Now take all those numbers (one 2, one 3, one 5) and multiply them together to get the GCF.

2*3*5 = 30, so 30 is the GCF of 90 and 480.

There's way too many problems here for me to do them all. You should try doing these yourself, as practicing with math problems is the only good way to learn math.

Good luck!

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