Other Topics Puzzle – Challenge 97
This is a great mathematics puzzle and brain teaser which contains some mathematical content. Can you solve it? The full solution is also given.
Challenge:
What is the smallest positive integer that has 7 factors?
The Absolute Best Book to Challenge Your Smart Student!
The correct answer is 64.
To find the answer, we can factorize numbers from 1, one by one. But, it takes for ever!
Every integer N is the product of powers of prime numbers:
N \(= P^{a}Q^{b}…R^{y}\)
Where P, Q, …,R are prime numbers and a, b, …, y are positive integers.
If N is a power of a prime, then N \(= p^{α}\), therefore, it has α + 1 factors.
If N \(= P^{a}Q^{b}…R^{y}\), then, N has (a+1) (b+1) … (y+1) factors.
To find the smallest number that has 7 factors, first write the factors of seven: 7 = 1 × 7
It means that the number in this question has just one prime factor in its decomposition – one with the exponent of α = 6. Keep in mind that b = 0, and \(Q^{b} = Q^{0} = 1\)
N \(= P^{6}Q^{0}\). To make N as small as possible, we have to choose the smallest available prime 2. The answer is obviously \(N = 2^{6} = 64\).
The seven factors of 64 are: 1, 2, 4, 8, 16, 32 and 64
The Best Books to Ace Algebra
Related to This Article
More math articles
- Top 10 3rd Grade Georgia Milestones Assessment System Math Practice Questions
- 6th Grade Georgia Milestones Assessment System Math FREE Sample Practice Questions
- Linear, Quadratic, and Exponential Models
- Top 10 Tips to ACE the CBEST Math Test
- Full-Length 8th Grade FSA Math Practice Test
- Overview of the CLEP College Mathematics Test
- Geometry Puzzle – Critical Thinking 18
- How to Graph Linear Inequalities? (+FREE Worksheet!)
- The Best Webcams for Teachers and Online Students
- What are the Similarity Criteria? Exploring the Fundamentals of Shape Proportions in Geometry
What people say about "Other Topics Puzzle – Challenge 97 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.