Question

James has 40 blue marbles and Sam has 48 yellow marbles. They divide the marbles into small pouches with an equal number of marbles in each pouch without any remainder. What is the largest possible number of marbles in each pouch?

a) 4
b) 6
c) 8
d) 10

Answer 1

The largest number of marbles that can be evenly divided into pouches from both James' and Sam's collections is found by calculating the greatest common divisor of 40 and 48, which is 8. Thus, each pouch can contain 8 marbles.

Step-by-step explanation:

The question relates to finding the largest number of marbles that can be evenly placed into pouches for both James’ and Sam’s collections of marbles. To determine this, we need to find the greatest common divisor (GCD) of the number of blue marbles James has (40) and the number of yellow marbles Sam has (48).

The GCD of 40 and 48 is found by listing the factors of each number or by using the Euclidean algorithm. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40, and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest number that appears in both lists is 8, so the greatest number of marbles that can be placed in each pouch is 8 marbles without any remainder.

The correct answer from the options provided is: c) 8.