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MIDDLE SCHOOL

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

Working with variables?
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.



Find Pairs of Positive Integers [10/15/2001]
Find pairs of positive integers whose greatest common factor is 1 and whose sum is 2000.

Find the Smallest Number... [10/21/1997]
... that has factors of 1, 2, 3, 4, 5, 6, 7, and 8.

Five to the Third Power [09/20/2001]
What is 5 to the 3rd power? I put 15. Wrong!

Formula for Greatest Common Divisor [01/08/1997]
Is there a formula to get the greatest common factor?

Greatest Common Factor [06/02/1999]
Given their GCF, how can I find an even and an odd number such that one is not a multiple of the other?

Great Explanation of How to Find the Least Common Multiple [10/24/2007]
One alarm clock rings every 25 minutes, another every 30 minutes, and another every 35 minutes. How long will it take for all three clocks to ring at the same time?

Help with Factoring [4/14/1996]
I've just started and can't figure out a logical way to get the hang of factoring.

How Many Factor Pairs Does a Given Number Have? [03/19/2004]
I'm wondering if there is a formula or algorithm that will tell me exactly how many pairs of factors a number has?

How Many Pads of Paper? [10/30/2001]
A merchant marked some pads of paper down from $2.00 and sold the entire lot. If the gross profit from the sale was $603.77, how many pads did he sell?

How to Find the Prime Factorization of a Whole Number [11/29/2005]
I'm really confused about how to find the prime factorization of a number. Can you help me?

Impossible Word [04/14/2001]
What word comes out to 575,151 when you multiply together the values of its letters?

Integer Divisors [04/11/1997]
N has six distinct integer divisors including 1 and N. The product of five of these is 648; find another divisor of N.

Investigating Prime Factors as a Classroom Activity [06/27/2004]
If n is a composite number, is it true that all prime factors of n must not exceed the square root of n?

Laps and Least Common Multiples [05/24/2002]
Three people are running around a track at different speeds. When will they all return to the starting point at the same time?

Layers of Least Common Multiples [10/13/2012]
How does the "upside-down birthday cake method" work? Doctor Ian unpacks this method for determining least common multiples, and compares it with conventional prime factorization.

LCM 120, HCF 4 [01/24/2002]
Find three examples of two numbers if their LCM is 120 and their HCF is 4.

LCM and GCF, Combined: Why and How [12/20/2010]
A student familiar with simultaneously calculating the least common multiple (LCM) and greatest common factor (GCF), as shared on Ask Dr. Math, re-visits the all-in-one method. Doctor Peterson expands on his earlier explanation of the technique, then extends it to apply to three numbers.

Least Common Multiple [09/29/2001]
What is the least common multiple of 11, 13, and 17?

Least Common Multiple, 2-10 [10/28/2002]
Find the smallest counting number that is divisible by the numbers 2 through 10.

Least Common Multiple Word Problem [12/10/1996]
Each of three businesses receives different sized cartons of glasses. If all three receive the same number of glasses and none of them receive more than a thousand glasses, how many glasses and cartons are in each shipment?

Making a Factor Tree [03/26/1998]
How do you make a factor tree?

Mental Math [07/25/2003]
I would like to find a trick for multiplying by 3367.

Multiples and Factors [06/02/2003]
What is the difference between multiples and factors?

Multiplicand, Multiplier [07/05/2001]
Do you agree with me that in the following mathematical sentence: 456x10, 456 is called the multiplicand and 10 is called the multiplier?

Multiplying Fractions [02/06/2001]
I need help solving 8/9 * 3/5. What is cross-cancelling?

Numbers with 5 Factors [02/06/2002]
I know that 16 has 5 factors (1,2,4,8,16). What other two numbers might have 5 factors?

One Approach to Finding LCM and GCF at the Same Time [03/02/2006]
I just learned a way of using a chart that lets you find the LCM and the GCF for two numbers at the same time, quickly and easily. Here it is!

One Billion as Product of Two Numbers with No Zeros [12/12/2001]
Write 1,000,000,000 as the product of two numbers, neither of which contains any zeros.

Precise Numbers [10/18/2001]
A precise number occurs when its proper divisors multiplied together equal the number: 6 is a precise number because 1*2*3 = 6. Is there another name or formula?

Prime Factoring Large Numbers [03/28/2003]
What are the prime factors of 5515596313?

Prime Factorization [01/07/1997]
How do you find the prime factorization of a number?

Prime Factor Puzzle [10/24/2003]
The two prime factors of a number are greater than 12 but less than 25. The number is greater than 300 but less than 400. What is the number? What are the factors?

Prime Factors [01/28/2006]
What is a number with only two prime factors and no repeated factors?

Prime Factors as Bricks [10/26/2001]
Is there another way to find prime factors besides making a factor tree?

Prime Factors of 4,194,305 [09/20/1999]
How can I find the prime factors of 2^22+1?

Prime Number Puzzle [09/27/2001]
I am the product of four primes, and the sum of these numbers is thirty. My three digits are prime and different. What number am I?

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?

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