Tricky Farm Math: How Many Groups Can the Farmer Make? #shorts #mathstricks #challenges #math
2A farmer has 30 sheep and 28 chickens. He wants to separate them into equal groups with no animals left over. What is the largest possible number of groups he can create?
The answer might seem straightforward at first glance, but there's a trick to it. The largest possible number of equal groups the farmer can create is actually one! Here's how:
First, note that both 30 and 28 are even numbers, so we can divide each by 2 to get 15 and 14.
Now, if we try to divide 15 sheep and 14 chickens into equal groups, we'll notice that we can only create one group. That's because the greatest common divisor (GCD) of 15 and 14 is 1. In other words, 15 and 14 are relatively prime.
If two numbers are relatively prime, it means they have no common divisors other than 1. That, in turn, means that any two equal groups we create must contain both sheep and chickens, because neither 15 nor 14 is divisible by the other.
So, we can put all 30 sheep and 28 chickens in one big group and call it a day!
Congratulations if you got the answer right, and I hope you enjoyed the challenge!