Question 900647: 1.how many factors do 18 and 24 have in common?
a.6 b.5 c.4 d.3 e.2
2. Which of the following numbers leaves a remainder when divided by 9?
a.369 b.9513 c.8181 d.10,919 e.84,843
3. Which of the following could be the remainders when three consecutive odd integers are divided by 5?
a.4,1,3 b.1,2,4 c.2,0,4 d.0,2,3 e.0,3,4
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Highlighting the factors in common
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The two numbers have 4 factors in common. So the answer is choice c) 4.
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# 2
Add up the digits: 369 ---> 3+6+9 = 9+9 = 18
18 is a multiple of 9, so 369 is also a multiple of 9
That means 369/9 has a remainder of 0.
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8181 ----> 8+1+8+1 = 9+9 = 18
So 8181/9 has a remainder of 0.
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10919 ----> 1+0+9+1+9 = 20
20/9 has a remainder that is nonzero (turns out it is 20-18 = 2)
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84843 ----> 8+4+8+4+3 = 27
27/9 has a remainder of 0.
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Final Answer: choice D) 10919
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# 3
Consecutive odd integers are integers like: 11, 13, 15
They are odd and they are the closest to one another possible and follow in sequence.
We'll cycle through a list of possible choices until we get to the answer
Consecutive Odd Integers: 1, 3, 5
1/5 = 0 remainder 1
3/5 = 0 remainder 3
5/5 = 1 remainder 0
So we get the remainders 1, 3, 0
This choice isn't listed, so we move on.
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Consecutive Odd Integers: 3, 5, 7
3/5 = 0 remainder 3
5/5 = 1 remainder 0
7/5 = 1 remainder 2
So we get the remainders 3, 0, 2
This choice isn't listed, so we move on.
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Consecutive Odd Integers: 5, 7, 9
5/5 = 1 remainder 0
7/5 = 1 remainder 2
9/5 = 1 remainder 4
So we get the remainders 0, 2, 4
This choice isn't listed, so we move on.
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Consecutive Odd Integers: 7, 9, 11
7/5 = 1 remainder 2
9/5 = 1 remainder 4
11/5 = 2 remainder 1
So we get the remainders 2, 4, 1
This choice isn't listed, so we move on.
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Consecutive Odd Integers: 9, 11, 13
9/5 = 1 remainder 4
11/5 = 2 remainder 1
13/5 = 2 remainder 3
So we get the remainders 4, 1, 3
This is listed as an answer choice, which is choice A
The final answer is choice A) 4, 1, 3
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