Learning Goals We will use our divisibility rules so that we can decompose numbers into prime factors Well know we understand when we can identify the prime factors that are used to form a number ID: 592867
Download Presentation The PPT/PDF document "Decomposing a Number into Prime Factors" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Decomposing a Number into Prime FactorsSlide2
Learning Goals
We will use our divisibility rules so that we can decompose numbers into prime factors.
We’ll know we understand when we can identify the prime factors that are used to form a number.Slide3
Vocabulary
Composite number
Divisibility
Division
Divisor
Factor / Prime factor
Prime numberSlide4
Use Your Divisibility Rules
A number is
divisible by 2
if the
last digit is even
(0, 2, 4, 6, or 8)
A number is
divisible by 3
if the
sum of all the digits in the number is divisible by 3
.
A number is
divisible by 5
if the
last digit is 0 or 5.
A number is
divisible by 10
if the
last digit is 0.Slide5
Use Your Divisibility Rules
A number is
divisible by 4
if the
last 2 digits are both 0 or if they are divisible by 4 or 2 twice
.
A number is
divisible by 6
if it is
divisible by 2 and by 3
(i.e. if it ends in an even number and if the sum of its digits is divisible by 3).
A number is
divisible by 8
if the
last 3 digits are all 0 or if the number they form is divisible by 4
.
A number is
divisible by 9
if the
sum of its digits is
divisible by 9
.Slide6
Decomposing a Number into Prime Factors
A decomposed (or factorized) number means that it is only represented by
prime numbers
.
Use your divisibility rules to help you find the prime factorization of a number.
A number’s
factors
are also its
divisors
.
Remember: a prime number has only 2 divisors – 1 and itself (i.e. 2, 5, 23, etc.)
The divisors of 64 are {1, 2, 4, 8, 16, 32, 64}. 2 is its only prime factor.Slide7
Decomposing a Number into Prime Factors
Find 2 factors of the number to be decomposed.
If any of these are prime numbers, move on to the next number.
Reduce all numbers to prime factors.
Always remember to use exponents to represent prime factors that appear more than once.
Always remember to arrange your factors in increasing order.
740
10 x 74
2 x 5 x 2 x 37
740 = 2
2
x 5 x 37