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Word Problems

Browse Middle School Factoring Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

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Try Middle School Factoring Expressions.

Selected answers to common questions:
    Finding a least common denominator (LCD).
    LCM, GCF.
    Prime factoring.
    Table of factors 1-60.

Prime Numbers vs. Prime Factors [01/13/1997]
What is the difference between a prime number and a prime factor?

Probability That a Sum Is Divisible by Three [11/04/2009]
How many ways can you choose three numbers from 1-100 whose sum is divisible by three?

Product a Perfect Cube [12/07/2002]
What is the smallest positive integer by which you can multiply 735 so that the product is a perfect cube?

Product Equal to 12 [04/09/2003]
How many different numbers have a product equal to 12?

Product of Numbers 1-100 [02/23/2002]
I was wondering how to find out how many zeros will be at the end of the product of all the numbers from 1 to 100 without multiplying them all out.

Product of Powers, Number of Divisors [04/26/2016]
A teen wonders why the exponents in an integer's prime factorization have anything to do with its divisor count. Doctor Ian introduces a binary model to make the connection; Doctor Greenie follows up with an algebraic explanation.

Product-Perfect Numbers [02/26/2001]
Is there a statement that describes product-perfect numbers?

Products of Digits [03/02/2003]
The product of digits in the number 234 is 24: 2*3*4 = 24. Can you describe a general procedure for figuring out how many x-digit numbers have a product equal to p, where x and p are counting numbers? How many different three-digit numbers have a product equal to 12? to 18? Why?

Rectangles and Factors [09/09/1998]
How many rectangles can you make with 10 small squares? 5 small squares? 12 small squares?

Rectangular Solids from Blocks [09/25/1998]
How many rectangular solids can be made from "n" cube-shaped blocks?

Reducing Fractions [7/4/1996]
How do you reduce fractions with different denominators?

Relatively Prime [10/07/1999]
What does the term relatively prime mean, and how can you determine if two numbers are relative primes?

The Sieve, and Ceiling, of Eratosthenes [07/27/2012]
Before introducing children to the sieve of Eratosthenes, a parent seeks to reconcile different methods found online. Doctor Peterson sees a didactic opportunity in the discrepant steps: how many factors do you actually need to check?

Simplifying Fractions [12/08/2002]
Finding and eliminating (cancelling) prime factors.

Simplifying Fractions by Factorizing [05/22/1998]
Using factor trees to prime factor and simplify 188/240.

The Smallest Number Which When Divided Leaves Specific Remainders [02/27/2010]
Doctor Rick, an eleven year-old, and her father apply least common multiples, modular arithmetic, and the Chinese Remainder Theorem to reason their way to the smallest number which when divided by 3, 7, and 11 leaves remainders 1, 6, and 5, respectively.

Table of Factors 1-60 [10/23/2001]
Where can I find a factor sheet with the factors 1 - 100?

Thinking about Number Pattern Problems [08/09/2004]
How do I figure out the next 2 numbers in the pattern 1, 8, 27, 64, ____, ____?

Tips for Simplifying Fractions [06/03/1998]
Can you give my some tips to help me simplify fractions?

Two Mathematicians: Factoring Logic [03/24/2003]
Two mathematicians are each assigned a positive integer. They are told that the product of the two numbers is either 8 or 16. Neither knows the other's number...

Unknown Numbers and a Venn Diagram [11/26/2001]
The GCF of two numbers is 20 and the LCM is 840. One of the numbers is 120. Explain how to find the other number and use the Venn diagram method to illustrate.

Using Euclid's Algorithm with Three Numbers [11/05/2003]
How do I find the GCD of three integers using Euclid's Algorithm? I am not sure where you plug the third integer into the algorithm.

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