Finding the Simplest Form (Greatest Common Divisor) of 88 and 72
The simplest form of two numbers refers to their ratio expressed in the lowest terms. This is achieved by finding the greatest common divisor (GCD) of the two numbers and dividing both numbers by it.
Let's find the simplest form of 88 and 72:
1. Finding the Greatest Common Divisor (GCD):
There are several methods to find the GCD. We'll use the Euclidean algorithm, a relatively simple and efficient method:
- Divide the larger number (88) by the smaller number (72): 88 ÷ 72 = 1 with a remainder of 16.
- Replace the larger number with the smaller number (72) and the smaller number with the remainder (16): Now we have 72 and 16.
- Repeat the process: 72 ÷ 16 = 4 with a remainder of 8.
- Repeat again: 16 ÷ 8 = 2 with a remainder of 0.
The last non-zero remainder is the GCD. In this case, the GCD of 88 and 72 is 8.
2. Simplifying the Ratio:
Now that we have the GCD, we divide both 88 and 72 by 8:
- 88 ÷ 8 = 11
- 72 ÷ 8 = 9
Therefore, the simplest form of 88 and 72 is 11:9. This means that the ratio 88:72 is equivalent to the ratio 11:9. Both ratios represent the same proportion.
