What is #12414/155679# in simplest form?

Question

Jeremiah Andrews · Accepted Answer

#12414/155679 = 4138/51893#

One method of finding the greatest common factor (GCF) of two numbers goes as follows:

Divide the larger number by the smaller to give a quotient and remainder.

If the remainder is #0# then the smaller number is the GCF.

Otherwise repeat with the smaller number and the remainder.

In our example, we can find the GCF of #12414# and #155679# as follows:

#155679/12414 = 12" "# with remainder #6711#

#12414/6711 = 1" "# with remainder #5703#

#6711/5703 = 1" "# with remainder #1008#

#5703/1008 = 5" "# with remainder #663#

#1008/663 = 1" "# with remainder #345#

#663/345 = 1" "# with remainder #318#

#345/318 = 1" "# with remainder #27#

#318/27 = 11" "# with remainder #21#

#27/21 = 1" "# with remainder #6#

#21/6 = 3" "# with remainder #3#

#6/3 = 2" "# with remainder #0#

So the GCF is #3#

So:

#12414/155679 = (12414/3)/(155679/3) = 4138/51893#

This is in simplest form.

Noah Archer · Answer

#12414/155679=4138/51893#

We have: #12414/155679#

To reduce this to simplest form, we can try estimating to find a possible factor of the expression. These numbers are well past any times tables I ever learned.

Right away, we can see that #2# is not a factor since we have even and odd numbers in the numerator and denominator.

But #3# does look promising since the first part of both numbers divide by #3# and maybe the last part as well.

Then: #12414/155679=(12414/3)/(155679/3)=4138/51893#

Can we go farther? We can see that again #2# is not a factor of both since it will not divide evenly into #51893#.

Lets try #3#: #51893/3=17297.67# so we are done.

Aurora Arias · Answer

undefined To express the fraction 12414/155679 in simplest form, you can find the greatest common divisor (GCD) of the numerator and denominator, which is 3. Divide both the numerator and denominator by this GCD:
12414 ÷ 3 = 4138
155679 ÷ 3 = 51893

So, the simplest form of 12414/155679 is 4138/51893.