Jessica can cut two strings into equal lengths by finding the greatest common divisor (GCD) of their lengths. The strings can be cut into 8 equal lengths of 16 centimeters each.
Jessica has two strings, and she wants to cut them into equal lengths. To find the maximum number of equal lengths she can cut, we need to determine the greatest common divisor (GCD) of the lengths of the two strings. The first string measures 80 centimeters and the second string 64 centimeters.
Step 1: Find the GCD of 80 and 64. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80, and the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. The largest common factor is 16.
Step 2: Divide the lengths of both strings by the GCD. For the first string: 80 cm / 16 = 5 lengths. For the second string: 64 cm / 16 = 4 lengths. Since both strings have to be cut into equal lengths, the maximum number of equal lengths for both strings is the smaller number, which is 4.
The correct main answer is: B) 8 lengths. Each length will be 16 centimeters.
To maximize the number of equal lengths, Jessica can cut both strings into equal lengths of 16 centimeters, ending up with a total of 8 lengths.