Thursday

November 20, 2014

November 20, 2014

Posted by **kim** on Wednesday, April 18, 2007 at 8:59pm.

385 = 5 x 7 x 11

1365 = 3 x 5 x 7 x 13

which factors are found in both?

5 x 7

so 35 is the HCF, (it's like taking the intersection of the elements of two sets)

There are two methods. The first one is the brute force method where you just factor each of the numbers in prome factors and see which prime factors they have in common.

385 = 5 * 7 * 11

1365 = 3 * 5 * 7 * 13

So, the greatest common factor (a.k.a. GCD or gretest common divisor) is 5 * 7 = 35

But there is another (much faster for large numbers) method that doesn't involve factorization. Since the GCD of two nu,mbers doesn't change when you replace one of the numbers b a linear combination of the two numbers you can subtract from the largests of the two numbers a multiple times the smallest number so that it becomes smaller than the smallest if the two. If you repeat this process with now the new numbers, then the numbers will become smaller and smaller until you end up with a trivial case.

GCD(385, 1365) =

GCD(1365 - 3*385, 385) =

GCD(210, 385) =

GCD(385-210,210) =

GCD(175,210) =

GCD(35,175) =

GCD(0,35) = 35

**Answer this Question**

**Related Questions**

math - help please find the greatest common factor of 385 and 1365. 385=5x7x11 ...

Greatest Common factors - I dont know these answers. Can you help me? Greatest ...

Algebra - I need a step by step explanation of finding the GCF of (6ysquare -3y...

Physical Science - The specific heat of copper is 0.385 J/g.°C. Which equation ...

Math- help please - what is the greatest common factor of 245, 385, and 539

science - 12. The specific heat of copper is 0.385 J/g • °C. Which equation ...

math,help - Can someone show me how step by step how to solve this problem... ...

Math - list the common factors for each pair of numbers. Then find the greatest ...

Math - For Exercises 16 - 23, list the common factors for each pair of numbers. ...

math - Is The factors of 385 = 1,5,7,55,77,385?