# 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

### Units of physical quantities:

#### Themes, topics:

### Grade of the word problem:

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