# Tag Archives: prime factorization

## Sums of Reciprocals

The sum of the positive divisors of is . Find the sum of the reciprocals of the positive divisors of . Source: NCTM Mathematics Teacher, February 2008 Solution Given that , the number of divisors is . The first twelve … Continue reading

## Smaller Factor

Given a three-digit number, interchange the units digit and the hundreds digit. The product of the original number and the new number is . What is the smaller three-digit factor? Source: NCTM Mathematics Teacher, February 2008 Solution Since the product … Continue reading

## Set of Primes

Let be the set of primes that divide . What is the largest integer so that the set of primes that divides is equal to ? Source: NCTM Mathematics Teacher, August 2006 Solution The next prime greater than is . … Continue reading

## Partners in Integers

Two integers are said to be partners if both are divisible by the same set of prime numbers. Find the number of positive integer less than that have no partners less than . Source: NCTM Mathematics Teacher, August 2006 Solution … Continue reading

## Product of Consecutive Integers

How many integer pairs satisfy the equation ? Source: NCTM Mathematics Teacher, September 2006 Solution We construct products of positive consecutive integers and see which ones if any can be expressed as a power of . is the only such … Continue reading

## Cute Number

A number is called cute if it has exactly four positive integral divisors. What percent of the first twenty-five positive integers are cute? Source: NCTM Mathematics Teacher, January 2006 SOLUTION number of factors/divisors Other integers that have factors/divisors: . Total number … Continue reading

## Prime Factors

Find the prime factors of . Source: NCTM Mathematics Teacher, January 2006 SOLUTION Recall that Both and are prime numbers. The prime factors of are and . Answer: and