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
- Full-Length ATI TEAS 7 Math Practice Test
- The Ultimate Common Core Algebra 1 Course (+FREE Worksheets)
- Compare the Temperatures Above and Below Zero
- Mastering the Lagrange Error Bound for Reliable Function Approximations
- How to Find the Axis of Symmetry of Quadratic Functions?
- Full-Length ISEE Middle Level Math Practice Test
- Customary Unit Conversions Involving Mixed Numbers and Fractions
- Using a Fraction to Write down a Ratio
- How to Find Rational and Irrational Numbers?
- Unlock the Gateway to Academic Achievement: “OAR Math for Beginners” Comprehensive Solution Manual
What people say about "Other Topics Puzzle – Challenge 97 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.