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Prime factorization | Factors and multiples | Pre-Algebra | Khan Academy

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Prime Factorization - 5th Grade Math - Finding Factors of a Number (Factoring) - Math Homework Help!

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Today's lesson in my 7th grade math class was on finding the greatest common factor and least common multiple of a pair of numbers.

I started by gathering background information about what the students already knew about the GCF and LCM. With a little bit of help the students were able to come up with definitions for each of them and described the method they had used in the past to find the greatest common factor and least common multiple of two numbers.

Previously the students had learned to list all the factors of 2 numbers and find the largest one they had in common. Similarly, to find the least common multiple, the class had learned to list multiples of the numbers until they found one in common.

We went through examples of finding the GCF and LCM the "old school" way.

Then we discussed the limitations of this method for finding the GCF and LCM, mainly the fact that if I gave them much larger numbers it would be very time-consuming to list all the factors or list multiples until they found one in common. So...I then introduced the class to the "Cake Method". (Alot of people refer to it as the ladder method or division ladder, but I first saw it called the cake method in the book Math Doesn't Suck by Danika McKellar, and I thought it was cute, so that is what I go by, since it resembles an upside-down cake).

The cake method is great for a couple of different reasons...you can make one "cake" and use it to find both the GCF and the LCM and it saves you alot of time over the more traditional method.

For anyone who hasn't seen this method before, you start by writing the numbers for which you are trying to find the GCF and LCM next to each other and draw a "layer of cake" around them. You then find ANY common factor of the two numbers and write that factor to the left of them. You then divide the numbers by their common factor and write the quotients underneath the numbers. This process repeats then with the new 2 numbers you have inside the cake. You do this as many times as necessary until the 2 numbers at the bottom are relatively prime. To find the greatest common factor, you multiply all the numbers to the left of the cake. To find the LCM, I tell the students to draw a big "L" around the cake, and multiply all the numbers in the "L" together.

Here is the example we did in class to find the GCF and LCM of 24 and 36.

We had a discussion about how different people could make different "cakes" by choosing different factors, but that the final answer would be the same. We also discussed how the bigger the factor, the less layers of cake there would be.

Overall, the lesson went great! The students loved this "new" method of finding the GCF and LCM!

I am looking forward to showing them how the cake method can be used to simplify fractions, too. (Make a cake for the numerator and denominator and the 2 relatively prime numbers at the bottom will be the simplified fraction. For example, the cake example above could have been used to simplify the fraction 24/36 to 2/3.)

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Finding the GCF and LCM using the Cake Method - Math in the Middle

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Today's lesson in my 7th grade math class was on finding the greatest common factor and least common multiple of a pair of numbers. I started by gathering background information about what the students already knew about the GCF and LCM.

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Posts tagged 'cake method'

Today is my 2 year blogiversary and my 660th post. Thank you to all my readers and followers. I really appreciate all of you.

What better way is there to celebrate than with a gorgeous cake? Enjoy!

The cake method of finding prime factors makes a beautiful cake for the number 660 because 660 has several prime factors and the largest one, 11, looks like a couple of candles to top it off perfectly.

660 has a lot of factors, 24 in fact. 660 is a special number for several reasons:

No number less than 660 has more factors than it does, but 360, 420, 480, 504, 540, 600, and 630 each have just as many.

660 has so many factors that it seems natural for it to between twin primes, 659 and 661.

660 is the hypotenuse of the Pythagorean triple 396-528-660. What is the greatest common factor of those three numbers?

660 is the sum of consecutive prime numbers three different ways. Prime number 101 is in two of those ways:

157 + 163 + 167 + 173 = 660

101 + 103 + 107 + 109 + 113 + 127 = 660

67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 = 660

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660 is a composite number.

Prime factorization: 660 = 2 x 2 x 3 x 5 x 11, which can be written 660 = (2^2) x 3 x 5 x 11

The exponents in the prime factorization are 1, 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1)(1 + 1) = 2 x 3 x 2 x 2 = 24. Therefore 660 has exactly 24 factors.

Factors of 660: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660

Factor pairs: 660 = 1 x 660, 2 x 330, 3 x 220, 4 x 165, 5 x 132, 6 x 110, 10 x 66, 11 x 60, 12 x 55, 15 x 44, 20 x 33, or 22 x 30

Taking the factor pair with the largest square number factor, we get √660 = (√4)(√165) = 2√165 ≈ 25.690465.

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Did you know that the sum of all the prime numbers between 100 and 110 equals 420? Yes, 101 + 103 + 107 + 109 = 420.

Since 20 × 21 = 420, we know that 420 is the sum of the first 20 EVEN numbers. Thus,

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30 + 32 + 34 + 36 + 38 + 40 = 420.

420 is the smallest number that can be divided evenly by all the natural numbers from 1 to 7.

420 has a LOT of factors, more than most people would think it does. In fact, of all of the numbers from 1 to 420, there is only one number, 360, that has as many factors as 420 has.

There are 4 different prime numbers that can divide evenly into 420. Here are those factor trees:

Many, but not all, of the factors of 420 are listed somewhere on those four trees.

420 is a composite number.

Prime factorization: 420 = 2 x 2 x 3 x 5 x 7, which can be written 420 = (2^2) x 3 x 5 x 7

The exponents in the prime factorization are 2, 1, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 x 2 = 24. Therefore 420 has exactly 24 factors.

Factors of 420: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420

Factor pairs: 420 = 1 x 420, 2 x 210, 3 x 140, 4 x 105, 5 x 84, 6 x 70, 7 x 60, 10 x 42, 12 x 35, 14 x 30, 15 x 28, or 20 x 21

Taking the factor pair with the largest square number factor, we get √420 = (√4)(√105) = 2√105 ≈ 20.4939

Each factor pair, except 1 x 420, can make its own factor tree. Here are some factor trees featuring the other seven factor pairs:

If I hadn't made all the prime numbers in red, it's possible that one or more of the prime numbers might get forgotten. That is why I prefer the cake method for finding the prime factorization of a number. All of the prime numbers are listed in numerical order on the outside of the cake.

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Posts tagged 'cake method' Today is my 2 year blogiversary and my 660th post. Thank you to all my readers and followers. I really appreciate all of you. What better way is there to celebrate than with a gorgeous cake? Enjoy!

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Math is fun

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Number Properties - identify prime factors

Common Core Connection for Grades 4, 5, 6

Determine whether a given whole number in the range 1-100 is prime or composite.
Find common factors and multiples.
Find the greatest common factor of two whole numbers less than or equal to 100.
Find the least common multiple of two whole numbers less than or equal to 12.

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Factor Trees and Prime Factorization | Math Playground

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Play Factor Trees at MathPlayground.com! Use prime factorization to find the GCF and LCM of number pairs.

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Factor tree game

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Find all prime factors of a composite number with our Factor Tree. This interactive game requires Adobe Flash Player.

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Expanded form to exponential form

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How Do You Convert a Number in Expanded Form into Exponential Form? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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Exponential notation can be seen as just a way to write expression like 8x8x8x8 in a more compact form. If you have the same number multiplied by itself a number of times then using the exponential notation you write the number, in your case 8, and then an "exponent" to indicate how many times you multiply 8 by itself.

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Exponents are presented by Math Goodies. Learn exponents at your own pace with in-depth instruction

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Example:  Write Repeated Multiplication in Exponential Form

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6th grade exponents and powers memory game

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6th grade exponents and powers memory game

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6th grade exponents and powers memory game for children to practice.

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In this Math Jeopardy game, students will practice solving problems about powers and exponents. Also, some problems involve identifying the base in a mathematical expression.