Find the greatest common divisor of 91 and 72.
$91 = 7^1 \cdot 13^1$ and $72 = 2^3 \cdot 3^2$, so gcd(91, 72) = $\boxed{1}$.
1
Level 2
Prealgebra
Problem: Find the greatest common divisor of 91 and 72.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the greatest common divisor (GCD) of two numbers, we can use the Euclidean algorithm. This method involves repeated division and finding remainders. 

First, we divide the larger number, 91, by the smaller number, 72. The division gives a quotient of 1 and a remainder of 19, since 91 = 72 * 1 + 19. 

Next, we apply the algorithm again, this time using 72 and the remainder 19. Dividing 72 by 19 gives a quotient of 3 and a remainder of 15, as 72 = 19 * 3 + 15.

We continue the process with 19 and 15. Dividing 19 by 15 results in a quotient of 1 and a remainder of 4, since 19 = 15 * 1 + 4.

Next, we take 15 and divide it by 4. This gives a quotient of 3 and a remainder of 3, as 15 = 4 * 3 + 3.

We then divide 4 by 3, yielding a quotient of 1 and a remainder of 1, since 4 = 3 * 1 + 1.

Finally, we divide 3 by 1, which results in a quotient of 3 and a remainder of 0, as 3 = 1 * 3 + 0. 

When the remainder reaches 0, the last non-zero remainder is the GCD. In this case, the last non-zero remainder is 1. 

Thus, the greatest common divisor of 91 and 72 is 1.<|END_OF_LATENT|> The final answer is $1$.