11 you cut a yellow cake into 6 pieces and a chocolate cake...

Name: 11 you cut a yellow cake into 6 pieces and a chocolate cake of the same size into 8 pieces then you find out that you were supposed to cut both cakes into the same unspecified number of piec 97542
Uploaded: 2024-04-30T21:38:25-08:00
Duration: 6 min 5 s
Channel: Matthew Winsor
Description: 11 you cut a yellow cake into 6 pieces and a chocolate cake of the same size into 8 pieces then you find out that you were supposed to cut both cakes into the same unspecified number of piec 97542

11. You cut a yellow cake into 6 pieces and a chocolate cake of the same size into 8 pieces. Then you find out that you were supposed to cut both cakes into the same (unspecified) number of pieces! As a number theory student, what do you do?

Transcript

00:01 Okay, so there's some information here we need to pull.

00:04 We need, we want, we see that we have bakery has 630 chocolate chip cookies and 702 peanut butter cookies.

00:20 And the bakers want to divide the chocolate chip cookies into piles and the peanut butter cookies into piles.

00:27 So that each pile has only one type of cookie.

00:30 There's the same number and there's the same number of cookies in each pile and each pile has the largest number of cookies so we're gonna make some piles of 630 and 702 each pile is going to be the same and it's going to be the biggest amount that there can be okay so i am hearing when i hear those things i i want to divide it, i'm looking for greatest common factor.

01:02 Okay, greatest common factor.

01:05 And if we're looking, so because the greatest common factor is the biggest number that divides into 630 and 702.

01:13 So we're looking for this number to tell how many is going to be in each pile.

01:17 And then when we divide those numbers, 630 and 702 by those numbers, it'll tell us how many piles there are.

01:25 Okay, so we need to do some, you know, the quickest way i know how to do it is to take 630 and do prime factorization.

01:39 So this is going to be 63 times 10.

01:43 You could have divided it by 2.

01:45 You could divide it by 5.

01:47 You could probably even divide it by 3, and it would work.

01:52 I'm just going to, i'm just doing this.

01:55 So 10 is 2 times 5 63 is what that's 3 times 21 which is 3 times 7 9 times 7 63 of course okay so we have 3 3 so we have 2 3 3 5 and 7 that's the that's time and these times okay let's look at 702 702 um she's you can divide it by 3 so 702 divided by 3 yes 3 goes into 6 2 7 0 2 7 3 2 6 1 2 that should be a 3 3 9 1 1, 4.

03:01 So we have 234...

Question

11. You cut a yellow cake into 6 pieces and a chocolate cake of the same size into 8 pieces. Then you find out that you were supposed to cut both cakes into the same (unspecified) number of pieces! As a number theory student, what do you do?

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