METHOD 1 – Prime Factoring
Reduce 36/60 to lowest terms .
• Factor the numerator and denominator into prime factors.
• Cancel common factors in numerator and denominator, and
multiply the remaining factors.
METHOD 2 – Divisibility
Reduce 36/60 to lowest terms.
• Using the divisibility hints on sheet 2, check for the
even divisibility of prime numbers into both
the numerator and denominator. Since 2 divides into both 36 & 60 evenly:
• Continue using the divisibility rules . Since 2 divides
into both 18 & 30 evenly:
• Finally, since 3 divides into both 9 & 15 evenly:
There are no remaining common prime factors, so the final
answer is .
HINTS FOR DIVISIBILITY OF SOME COMMON PRIME FACTORS


Example 
Check the last digit 
If even (0,2,4,6,8) Then number is
divisible by 2 
76 
6 is even 

Add all digits 
If the sum is divisible by 3 The
number is
divisible by 3 
123 
1+2+3=6
6 is divisible by 3 

Is the last digit 0 or 5? 
The number is divisible by 5 
415 
Last digit is 5 

Are all of the digits the
same? 
If there is an even number of digits,
the
number is divisible by 11. 
66 
All digits are the
same, and there
are an even
number of digits. 

Add up every other digit. 
If the sums are the same, the number
is
divisible by 11. 
253 
2+3=5
5=5 

Now, try the practice problems below.
PRACTICE PROBLEMS: Reduce the following fractions
to lowest terms.
Answers