GCF of 720 and 1500

GRE Quant Problem Solving
1

I am confused as to how greg is getting GCF for 720 and 1500 = 60

The prime factorization of 720 is 2^4, 3^2, 5^1
The prime factorization of 1500 is 2^2, 3^1, 5^3

They both share in common, 2^2, 3^1, 5^2 which totals up to a GCF of 300

I am not sure why on the video greg is getting prime factorization for 1500 = 2^2, 3^1, 5^2 when you perform prime factorization you get 5^3, I’m not sure why is isn’t counting one of the 5s when factoring it out

Video Week 1 day 1 Factors and Multiples, video time 52:20 min

2

300 is not the GCF, clearly! 720 isn’t divisible by 300. I think you mean 2^2.3^1.5^1 which gives a GCF of 60.

For what Greg does, I couldn’t find the explanation at the time stamp you’ve posted.

3

I’m not sure why he is getting 5^2 when factoring out 1500, you end up with 5^3. Why isn’t he counting that last 5. If you go to the video and watch him work out the problem you can see him leave out a 5 when completing the factoring of 1500. Pls help :(. Thanks!

4

But skipping the third power of 5 shouldn’t matter coz anyways you have the common factor as only the first power of 5. Don’t think about it too much. 60 is the GCF. There’s a customer support chat icon on the website, ping them with a screenshot of this and maybe Greg will add a note in the video saying this was a mistake.

5

I thought it was a mistake at first. But, if you include the 5 he left out while factoring 1500, you get 300 as the GCF. So, I think there is a reason as to why he left that 5 out. I just want to know because I encountered a practice problem that had the same issue. I wish he had more of an explanation.

6

Noooooooo :’)
How does the missed 5 matter? Tell me again

7

If you watch him solve that problem, he combines all the prime numbers. But, if you look at his work, you will see that he leaves out a 5 when factoring out 1500. So, my question is, why did he leave that 5 out. The true factored out 1500 = 2^2, 3^1, 5^3. But when greg writes it out, he writes down 2^2, 3^1, 5^2. I don’t get why he left out a 5. I want to know exactly why

8

That was probably a mistake. But either way the GCF shouldn’t have 5^2 is my point.

9

Hey guys, the answer is 60 - let me explain why.

The Prime Factorization of 720 is as follows:

720:
6: 2 x 3
X
120: 12 x 10 → 4 x 3 (12), 5 x 2 (10) → 2 x 2 (4)
Final: 2 x 2 x 2 x 2 x 3 x 3 x 5 – 2^4 x 3^2 x 5^1

1500:
150: 15 x 10 – 5 x 3 (15), 5 x 2 (10)
X
10: 5 x 2 (10)
Final: 2 x 2 x 3 x 5 x 5 x 5

He definitely made a mistake when listing the factorization of 1500

So if you look closely, the common bases and powers for both of those numbers are: 2^2 x 3^1 x 5^1

It is NOT 5^2 because 720 has only one 5, and 1500 has three 5s, so the number of 5 that is common for both is only one 5 which would be 5^1

Of course, if you multiply all of the commons together, you will get 60

I hope this helps!

11

Wow, literally stressed all day about how I wasn’t able to get the correct answer for such a simple math problem. I guess he did make a minor mistake listing the factors at the end which confused me. Now, I understand how he picked what both shared in common. I thought he was subtracting the “powers” to the numbers, which at the end would give you 5^2 when putting everything together. But instead you have to see what’s in “common”.