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- pilgrimpilot
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Number Properties, 3rd ed., p. 51 and answer on p. 53, no. 5
Is this an error? I show prime factors for 12 & 10 as 2, 2, 2, 3, & 5. The prime factor trees on p. 53 show the same but -> shows one less 2, changing the answer from YES to CANNOT BE DETERMINED. Please clarify.
- tommywallach
- Manhattan Prep Staff
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- Joined: Thu Mar 31, 2011 11:18 am
Re: Number Properties, 3rd ed., p. 51 and answer on p. 53, no. 5
Hey Pilgrim,
The text describes the reason. Their is a repetitive 2.
The best way to think of it is like this:
12 as a factor tells you: There are at least two 2s, and at least one 3.
10 tells you: There is at least one 2, and at least one 5.
When you put them together, you don't get three 2s. The fact that you have at least two 2s (the information from 12) already includes the information you got from the 10 (at least one 2).
It also may help to think of it this way. What is the LCM of 12 and 10? Obviously, it's 60. And what are the prime factors of 60?
60 --> 2 * 2 * 3 * 5 --> so you can see right there that the third 2 has disappeared.
Good luck!
-t
The text describes the reason. Their is a repetitive 2.
The best way to think of it is like this:
12 as a factor tells you: There are at least two 2s, and at least one 3.
10 tells you: There is at least one 2, and at least one 5.
When you put them together, you don't get three 2s. The fact that you have at least two 2s (the information from 12) already includes the information you got from the 10 (at least one 2).
It also may help to think of it this way. What is the LCM of 12 and 10? Obviously, it's 60. And what are the prime factors of 60?
60 --> 2 * 2 * 3 * 5 --> so you can see right there that the third 2 has disappeared.
Good luck!
-t
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