What is a fast way besides a factor tree to find the GCF?

Question

i rmber ine of my teachers sayung something about this trick it has to do with stairs and numbers and stuff

Answer 1

I only know of one other way. It's called the Euclidean algorithm.

Say you want to find the GCF of 144 and 96.

You take the bigger one and divide it by the smaller one: 144/96 = 1 remainder 48. So now your numbers are 96 and 48.

Divide 96 by 48 and you get 2 with no remainder. Therefore 48 is the greatest common factor.

Another example: 49 and 315.

315/49 = 6 remainder 21.

49/21 = 2 remainder 7.

21/7 = 3 remainder 0.

So 7 is the GCF.

A description of this process is given here:

http://www.krellinst.org/UCES/archive/modules/charlie/pke/node8.html

Answer 2

I assume you mean Greatest Common Factor.

I will give an example - 153 and 63. Do these subtractions:

153 - 63= 90
90 - 63 = 27
63 - 27 = 36
36 - 27 = 9
27 - 9 = 18
18 - 9 = 9
9 - 9 = 0,

so 9 is the GCF. The procedure is to take the second and third numbers of these subtractions and make them the first and second numbers of the next subtraction, making sure you subtract a lesser number from a greater. When you reach 0, the previous number is the GCF. If you reach 1, that's the GCF, and the numbers are relatively prime.

You can speed up the process by dividing and taking the quotient and remainder as the next two numbers each time, because division is a form of repeated subtraction.

Answer 3

I don't know about stairs and numbers but the fastest way is called the "Euclidean algorithm." Let's say your numbers are 75 and 27 (so the GCF is 3). You divide 75 by 27 to get a quotient of 2 and a remainder of 21. You shift the numbers over (dump the 75, use the 27 and 21---old divisor and the remainder). 27 divided by 21 is a quotient of 1 and a remainder of 6. Shift over, dump the 27, now use 21 and 6. 21 divided by 6 is 3 with a remainder of 3. Shift over, 6 divided by 3 is 2 with a remainder of 0. The last remainder before a remainder of zero is the GCF. That was 3.

Answer 4

the fastest way is to use prime numbers, 2,3,5,7,11 and so on. Divide both numerator and denominator by primes, usually 2, and 5 work, but sometimes you need to use others. Then when each has been reduced to it's prime, you can easily "collect" the primes in common to each, multiply them and find the GCF. Though this sounds complex, it isn't, it's really simple. Remember the fundamental rule of arithmetic, that all numbers that are not prime numbers have prime factors. Thus a number like 75 breaks down to primes of: 5 x 5 x 5, and 5 is a prime number; 55 breaks down to 5 x 11, two prime numbers. Usually you can break a number down to it's prime in your head. Try it with some of your homework and see how simple it is. So a fraction like 55 over 75 reduces quickly to 11 over 25 as the two common factors of 5 found in each go bye bye. With just a little practice it works in a flash. It's also grate for finding square roots when your calculator isn't handy. But that's another thing for a later lesson.

Answer 5

Just ask the question(s) on this site and ull have the answer in no time. It's kinda cheating but... what the hell right?

Answer 6

you can do a venn diagram or lcd's multiplied together i think

Answer 7

calculator