Question

9 Salvatore is making some back-to-school packs for his teacher. He has 96 pencils and 80 erasers. He wants each pack to be the same, and he wants to use all of the pencils and erasers. Find the greatest common factor of 96 and 80 to figure out how many packs he can make. How many pencils and erasers will be in each one?​

Answer 1

Explanation:

To find the greatest common factor (GCF) of 96 and 80, we can list their prime factors:

96 = 2^5 × 3

80 = 2^4 × 5

To find the GCF, we take the product of the common prime factors, using the lowest exponent for each factor that appears in both numbers. In this case, the only common factor is 2 raised to the power of 4, so:

GCF(96, 80) = 2^4 = 16

Therefore, Salvatore can make 16 packs, each containing the same number of pencils and erasers. To find out how many pencils and erasers will be in each pack, we divide the total number of pencils and erasers by the number of packs:

Number of pencils per pack = 96 pencils ÷ 16 packs = 6 pencils per pack

Number of erasers per pack = 80 erasers ÷ 16 packs = 5 erasers per pack

Therefore, each pack will contain 6 pencils and 5 erasers.