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Factors 73
Maths Review
April 28, 2014
PRIME FACTORS OF A NUMBER
FACT 1:
When a number is factored again and again until it cannot be factored any
further, then we have PRIME FACTORS.
In the example on the right, the factors of 24 are 4 and 6, which
can be factored again as follows
24 = 4 x 6 = (2 x 2) x (2 x 3) = 2 x 2 x 2 x 3
The factors 2 and 3 cannot be factored any further so we stop.
Similarly, we may show the prime factors of 60 as follows.
60 =
FACT 2:
4 x 15 =
(2 x 2) x (3 x 5)
=
2x2x3x5
The set of prime factors is unique to a number. No two numbers can have the
same set of prime factors.
“2, 3 and 7” are a unique set of prime factors for 42 because 2 x 3 x 7 = 42
“2, 2, 5 and 5” are a unique set of prime factors for 100 because 2 x 2 x 5 x 5 = 100
FACT 3:
The prime factors of a number may be determined by dividing the number by
prime numbers beginning with 2.
In this example, we determine the prime factors of 24 by successive
division. Note: The quotient is shown below the number.
We check the divisibility by 2, and divide as many times as possible.
24 = 2 x 2 x 2 x 3
In this next example, we determine the prime factors of 35574. One
divides by successive prime numbers until the quotient is also a
prime number. Each time one starts checking from the last divisor.
35574 = 2 · 3 · 7 · 7 · 11 · 11
1. Determine the prime factors of the following numbers.
9, 15, 18, 27, 36, 39, 49, 58, 64, 75, 88, 93, 100
2. The following are a unique set of prime factors of what number?
(a) 2 x 3 x 3
(c) 2 x 3 x 5
(e) 3 x 5 x 7
(b) 2 x 2 x 2 x 3
(d) 3 x 5 x 5
(f) 3 x 3 x 5
End of Lesson