Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400?
Correct answer:
Showing 1 comment:
Jason
Isn't the answer supposed to be 180?
Explanation:
The number of ways to split 2³ is 5C2, since we're looking at three integers which have their powers of 2 summing up to 3 i.e., a + b + c = 3 such that a,b,c >=0 and. x = pow(2,a), y = pow(2,b), z = pow(2,c). Similarly, the number of ways to split 5² is 4C2 and 7 is 3C2. So the total number of different ways to split 1400 into 3 integers should be 5C2*4C2*3C2, and hence 180.
Explanation:
The number of ways to split 2³ is 5C2, since we're looking at three integers which have their powers of 2 summing up to 3 i.e., a + b + c = 3 such that a,b,c >=0 and. x = pow(2,a), y = pow(2,b), z = pow(2,c). Similarly, the number of ways to split 5² is 4C2 and 7 is 3C2. So the total number of different ways to split 1400 into 3 integers should be 5C2*4C2*3C2, and hence 180.
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You need to know the following knowledge to solve this word math problem:
- combinatorics
- combinatorial number
- permutations
- multiplication principle
- permutations with repetition
- algebra
- prime numbers
- arithmetic
- multiplication
- division
- basic functions
- reason
- numbers
- natural numbers
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