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Q: What are two numbers whose sum is 38 and the smaller number is 14 less than the larger number?
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What is another name for a pair of numbers whose greatest common factor is the same as one of the numbers?

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Since one number is twice the other, the smaller number must be the greatest common factor. Since the greatest common factor is 7, that would make the other number 14. But, 7 is a prime number and has only one prime factor. However, the larger number, 14, has two prime factors. Also, the sum of the two numbers is 21, not 105. So, the information in the problem does not have a solution. Let us ignore the greatest common factor information. Let the smaller number be x. That means the larger number is 2x. x + 2x = 105 => 3x = 105 => x = 35. The two numbers are 35 and 70. The greatest common factor is 35. The smaller number, 35, has only two prime factors.


What is the number of 4 cm cubes which can be cut from the solid cube whose edge is 32 cm?

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