Aaron makes model airplanes using balsa wood. He has 14-and-35 inch strips of wood to cut into smaller pieces for wings. He wants to cut the strips into pieces of the same length. What is the longest whole number length he can cut?
The LCF of 14 and 35 is .... ?
To find the longest whole number length that Aaron can cut the strips into, we need to determine the greatest common divisor (GCD) of the two lengths of the strips, which are 14 and 35 inches.
The GCD is the largest number that divides both 14 and 35 without leaving a remainder. In this case, we can find the GCD using a few different methods, such as prime factorization, listing factors, or using the Euclidean algorithm. Let's use the Euclidean algorithm.
1. Start by dividing the larger number, 35, by the smaller number, 14:
35 ÷ 14 = 2 with a remainder of 7.
2. Now, divide the divisor from the previous step, which is 14, by the remainder, which is 7:
14 ÷ 7 = 2 with no remainder.
3. Continue the process by dividing the previous remainder, 7, by the remainder before it, 0.
7 ÷ 0 = undefined.
Since we got a remainder of 0, we stop the process. The last nonzero remainder, which is 7, is the GCD of 14 and 35.
Therefore, the longest whole number length that Aaron can cut the strips into is 7 inches.