Question

Find the greatest common factor (GCF) of 43 and 64 using repeated subtraction.

Answer 1

The greatest common factor (GCF) of 43 and 64 is found to be 1 by repeatedly subtracting the smaller number from the larger until we reach a point where the two numbers do not share any factors other than 1. This is because 43 is a prime number.

Step-by-step explanation:

To find the greatest common factor (GCF) of 43 and 64 using repeated subtraction, we follow these steps:

1. Subtract the smaller number (43) from the larger number (64) to get a new pair of numbers: 64 - 43 = 21, so now we work with 43 and 21.
2. Subtract the smaller number (21) from the larger number (43) to get a new pair: 43 - 21 = 22, so now we work with 21 and 22.
3. Since 21 and 22 are only one unit apart and we cannot subtract 21 from 22 anymore to get another number in common, we determine that they have no common factors besides 1.

Therefore, the GCF of 43 and 64 is 1, since 43 is a prime number and does not have any divisors other than 1 and itself.