Ray created the list of factors for 48 below.
48: 1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 48
Which number should be removed from his list to make the list accurate?
To determine which number should be removed from Ray's list to make it accurate, we need to understand what factors are.
Factors of a number are the whole numbers that can be evenly divided into that number without leaving a remainder. In other words, factors are the numbers that can be multiplied together to get the original number.
Let's examine Ray's list:
48: 1, 2, 3, 4, 6, 7, 8, 12, 16, 24, 48
To check if the list is accurate, we can start by multiplying each pair of numbers from the list and check if they equal 48. If there is a pair whose multiplication doesn't equal 48, then that number should be removed from the list.
Let's calculate the multiplication for each pair:
1 x 48 = 48 ✔️
2 x 24 = 48 ✔️
3 x 16 = 48 ✔️
4 x 12 = 48 ✔️
6 x 8 = 48 ✔️
7 x 6 ≈ 42 ❌
8 x 4 = 32 ❌
12 x 3 = 36 ❌
16 x 3 = 48 ✔️
24 x 2 = 48 ✔️
48 x 1 = 48 ✔️
From the calculations, we can see that there are three pairs that do not equal 48: 7 x 6, 8 x 4, and 12 x 3. Thus, the numbers 7, 8, and 12 should be removed from Ray's list to make it accurate.
To identify the incorrect number in Ray's list of factors for 48, we need to determine if any number is incorrectly included.
To do this, we can check each number in Ray's list to see if it is a factor of 48 by dividing 48 by the number. If the division result is an integer, then the number is a factor.
Let's go through Ray's list:
1: 48 ÷ 1 = 48 (integer result, so 1 is a factor of 48)
2: 48 ÷ 2 = 24 (integer result, so 2 is a factor of 48)
3: 48 ÷ 3 = 16 (integer result, so 3 is a factor of 48)
4: 48 ÷ 4 = 12 (integer result, so 4 is a factor of 48)
6: 48 ÷ 6 = 8 (integer result, so 6 is a factor of 48)
7: 48 ÷ 7 = 6.857142857142857 (not an integer result, so 7 is not a factor of 48)
8: 48 ÷ 8 = 6 (integer result, so 8 is a factor of 48)
12: 48 ÷ 12 = 4 (integer result, so 12 is a factor of 48)
16: 48 ÷ 16 = 3 (integer result, so 16 is a factor of 48)
24: 48 ÷ 24 = 2 (integer result, so 24 is a factor of 48)
48: 48 ÷ 48 = 1 (integer result, so 48 is a factor of 48)
From this analysis, we can see that 7 is incorrectly included in Ray's list. Therefore, 7 should be removed from his list to make it accurate.