Source: Manhattan Prep
How many factors greater than 1 do 120, 210, and 270 have in common?
A. One
B. Three
C. Six
D. Seven
E. Thirty
The OA is D
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How many factors greater than 1 do 120, 210, and 270 have in
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BTGmoderatorLU
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120 = 30*4BTGmoderatorLU wrote:Source: Manhattan Prep
How many factors greater than 1 do 120, 210, and 270 have in common?
A. One
B. Three
C. Six
D. Seven
E. Thirty
210 = 30*7
270 = 30*9
The GCF = the value in blue = 30.
Factors of 30 greater than 1:
2, 3, 5, 6, 10, 15, 30 --> 7 factors
Thus, 120, 210, and 270 have 7 common factors greater than 1.
The correct answer is D.
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Breaking each integer into its prime factors, we have:BTGmoderatorLU wrote:Source: Manhattan Prep
How many factors greater than 1 do 120, 210, and 270 have in common?
A. One
B. Three
C. Six
D. Seven
E. Thirty
The OA is D
120 = 12 x 10 = 2^2 x 3 x 5
210 = 21 x 10 = 2 x 3 x 5 x 7
270 = 27 x 10 = 2 x 3^2 x 5
We see that the 3 numbers have the following prime factors in common: 2^1 x 3^1 x 5^1. Adding 1 to each exponent produces (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 factors, including the number 1. So we have 7 factors that are greater than 1.
Answer: D
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