Question

45 students are on a school trip to the zoo.They need to split in to smaller groups of equal sizes.no student can be in a group alone.find all the possible group sizes from the numbers below.

6,9,1,45,4,5,3,15,11

Answer 1

The possible group sizes for 45 students without anyone being alone are 9, 45, 5, 3, and 15.

This is determined by dividing 45 by each number and finding whole number quotients.

Step-by-step explanation:

To find all the possible group sizes from the given numbers (6,9,1,45,4,5,3,15,11) for the 45 students on a zoo trip, we need to look for numbers that can divide 45 with no remainder, ensuring that no student is left without a group. We can do this by performing simple division.

• 45 ÷ 6 = 7.5 (not a whole number, so 6 is not a possible group size)
• 45 ÷ 9 = 5 (9 is a possible group size)
• 45 ÷ 1 = 45 (1 is a possible group size, but each student would be alone, so we disregard it)
• 45 ÷ 45 = 1 (45 is a possible group size, meaning no division into smaller groups)
• 45 ÷ 4 = 11.25 (not a whole number, so 4 is not a possible group size)
• 45 ÷ 5 = 9 (5 is a possible group size)
• 45 ÷ 3 = 15 (3 is a possible group size)
• 45 ÷ 15 = 3 (15 is a possible group size)
• 45 ÷ 11 = 4.09 (not a whole number, so 11 is not a possible group size)

Therefore, the possible group sizes, given the criteria, are 9, 45, 5, 3, and 15.

Group sizes of 6, 4, 1, and 11 don't allow for equal groupings without leaving students alone.