Factor
A factor of an integer is any
integer that divides the
given integer with no
remainder.
Prime Number
A prime number is a natural
number greater than one
that has exactly two positive
factors: one and itself.
Exercise
Tell whether 237 is divisible
by 2, 3, 4, 5, or 6.
3
Exercise
Tell whether 245 is divisible
by 2, 3, 4, 5, or 6.
5
Exercise
Tell whether 10,164 is
divisible by 2, 3, 4, 5, or 6.
2, 3, 4, 6
Exercise
Tell whether 111,222 is
divisible by 2, 3, 4, 5, or 6.
2, 3, 6
Exercise
State the divisibility test for 9.
Does 9 divide the
sum of the digits?
Fundamental Theorem of
Arithmetic
Every composite integer
greater than one can be
written as a product of prime
factors in exactly one way
(though the order of the
factors may vary).
Example 1
Write the prime factorization
of 42.
42
42 = 2 • 3 • 7
2 • 21
2 • 3 • 7
Example 2
Write the prime factorization
of 126.
2 126
3 63
3 21
7 7
1
126 = 2 • 32 • 7
Divide out all 2s,
then 3s,
then 5s,
and so on until the
quotient is prime.
Example 3
Write the prime factorization
of 90.
Example
Find the number whose
prime factorization is given.
23 x 3
24
Example
Find the number whose
prime factorization is given.
2x3x7
42
Example
Find the number whose
prime factorization is given.
5 x 72
245
Example
Find the number whose
prime factorization is given.
22 x 32 x 52 900
Example
Write the prime factorization
of the number.
126
2 x 32 x 7
Example
Write the prime factorization
of the number.
49
72
Example
Write the prime factorization
of the number.
625
54
Example
Write the prime factorization
of the number.
169
132
Example
Write the prime factorization
of the number.
200 23 × 52
Example
Write the prime factorization
of the number.
81
34
Exercise
Solve the equation to find the
missing prime factor.
273 = s • 7 • 13
s=3
Exercise
Solve the equation to find the
missing prime factor.
105 = 3 • 5 • n
n=7
Exercise
Solve the equation to find the
missing prime factor.
418 = 2 • c • 19
c = 11
Exercise
Solve the equation to find the
missing prime factor.
935 = 5 • 11 • y
y = 17
Exercise
Solve the equation to find the
missing prime factor.
238 = 2 • t • 17
t=7
Exercise
Solve the equation to find the
missing prime factor.
1,235 = y • 13 • 19 y = 5