Other Topics Puzzle – Challenge 97

Other Topics Puzzle – Challenge 97

This is a great mathematics puzzle and brain teaser which contain 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

Related to "Other Topics Puzzle – Challenge 97"

Other Topics Puzzle – Challenge 100
Other Topics Puzzle – Challenge 100
Other Topics Puzzle – Challenge 99
Other Topics Puzzle – Challenge 99
Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 98
Other Topics Puzzle – Challenge 96
Other Topics Puzzle – Challenge 96
Other Topics Puzzle – Challenge 95
Other Topics Puzzle – Challenge 95
Other Topics Puzzle – Challenge 94
Other Topics Puzzle – Challenge 94
Intelligent Math Puzzle – Challenge 93
Intelligent Math Puzzle – Challenge 93
Intelligent Math Puzzle – Challenge 92
Intelligent Math Puzzle – Challenge 92
Intelligent Math Puzzle – Challenge 91
Intelligent Math Puzzle – Challenge 91
Intelligent Math Puzzle – Challenge 90
Intelligent Math Puzzle – Challenge 90

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…