Question

relating factors and multiples ii - item 20048
which list shows only multiples of 8?
2, 4, 8
24, 32, 40
32, 96, 108
34, 42, 50

Explanation:

Step1: Recall the definition of a multiple

A multiple of a number \( n \) is a number that can be expressed as \( n \times k \), where \( k \) is a non - zero integer. So, to check if a number is a multiple of 8, we divide the number by 8 and see if the result is an integer.

Step2: Check the first list (2, 4, 8)

• For 2: \( 2\div8 = 0.25 \), which is not an integer. So 2 is not a multiple of 8.
• For 4: \( 4\div8=0.5 \), which is not an integer. So 4 is not a multiple of 8.
• For 8: \( 8\div8 = 1 \), which is an integer. But since 2 and 4 are not multiples of 8, this list is not correct.

Step3: Check the second list (24, 32, 40)

• For 24: \( 24\div8=3 \), which is an integer.
• For 32: \( 32\div8 = 4 \), which is an integer.
• For 40: \( 40\div8=5 \), which is an integer. So all numbers in this list are multiples of 8.

Step4: Check the third list (32, 96, 108)

• For 32: \( 32\div8 = 4 \), integer.
• For 96: \( 96\div8=12 \), integer.
• For 108: \( 108\div8 = 13.5 \), not an integer. So 108 is not a multiple of 8, this list is incorrect.

Step5: Check the fourth list (34, 42, 50)

• For 34: \( 34\div8 = 4.25 \), not an integer.
• For 42: \( 42\div8=5.25 \), not an integer.
• For 50: \( 50\div8 = 6.25 \), not an integer. So none of these numbers are multiples of 8.

Answer:

The list that shows only multiples of 8 is 24, 32, 40.