Download Decomposing a Number into Prime Factors

Decomposing a Number into
Prime Factors
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.
Vocabulary
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Composite number
Divisibility
Division
Divisor
Factor / Prime factor
Prime number
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.
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.
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.
Decomposing a Number into Prime
Factors
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2.
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5.
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
2 x 5
x
74
2 x 37
740 = 22 x 5 x 37