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Euclid's method is great for extremely large numbers - numbers which are extremely hard to factor. It doesn't require you to figure out the factors.I think the method is best explained with an example. Suppose you want the greatest common factor of 14 and 10.
This is the same as the gcf of 10 and 4 - where 4 is the REMAINDER of the division of 14 by 10 (if you divide 14 by 10, you get 1, with a reminder of 4).
Repeat: gcf(10, 4) = gcf(4, 2) - once again, the 2 is obtained as the remainder of the division, in this case, of 10 by 4.
gcf(4, 2) = gcf(2, 0) - in this case, the remainder is zero.
As soon as one of the numbers is zero, the other is the answer:
gcf(2, 0) = 2
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoEuclid's method is great for extremely large numbers - numbers which are extremely hard to factor. It doesn't require you to figure out the factors.
I think the method is best explained with an example. Suppose you want the greatest common factor of 14 and 10.This is the same as the gcf of 10 and 4 - where 4 is the REMAINDER of the division of 14 by 10 (if you divide 14 by 10, you get 1, with a reminder of 4).
Repeat: gcf(10, 4) = gcf(4, 2) - once again, the 2 is obtained as the remainder of the division, in this case, of 10 by 4.
gcf(4, 2) = gcf(2, 0) - in this case, the remainder is zero.
As soon as one of the numbers is zero, the other is the answer:
gcf(2, 0) = 2
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What is the greatest common factor of 24 and 71 using euclid's method?
Let's not bother Euclid. 71 is a prime number, its only factors are one and itself.The GCF of 24 and 71 is 1.
What is the largest common factor of 70 196?
The same as the greatest common factor of 70 and 26 - where 26 is the remainder of the division (196 divided by 70). Continue dividing, to get ever-smaller numbers - until one of the numbers is a multiple of the other. When this happens, the smaller of the numbers is the greatest common factor. This method is called the Euclid algorithm.
How many methods are there for the greatest common factor?
I guess the most common methods are the following: 1) List the common factors, and check which one is greatest. 2) Split each of the numbers into prime factors. Take all common factors and multiply them. 3) Euclid's algorithm. This method is fastest for large numbers.
What is the common factor of 105 and 161?
The greatest common factor of 161 and 105 is the same as the greatest common factor of 105 and 56. I obtained the number 56 by subtracting 161 - 151. Continue like this, until you get one number that is an exact multiple of the other. The next step is, 105 - 56 = 49, so you have to calculate the gcf of 56 and 49. This method is known as Euclid's Algorithm.
What is the greatest common factor of 121 and 132?
121: 11-11 132: 2-2-3-11 Great common factor: 11 Method(s) used: # (used) The method to find the greatest common factor of numbers is to find the prime factorizations of each one, select all matching prime factors, and then multiply. # An alternative method is to find all of the factors of each, and then select the greatest number that appears in each list. # The final method only applies to some numbers; if one of the number is a factor of the other, then that number is the greatest common factor. This is because all numbers are factors of themselves, and that is their greatest factor. If it is also a factor of the other number, then it is definitely the greatest common factor.
What is the greatest common factor of 196 and 1078?
196: 2-2-2-2-11 1078: 2-7-7-11 Greatest common factor: 22 Method(s) used: # The method to find the greatest common factor of numbers is to find the prime factorizations of each one, select all matching prime factors, and then multiply. # An alternative method is to find all of the factors of each, and then select the greatest number that appears in each list. # The final method only applies to some numbers; if one of the number is a factor of the other, then that number is the greatest common factor. This is because all numbers are factors of themselves, and that is their greatest factor. If it is also a factor of the other number, then it is definitely the greatest common factor.
What is the grates common factor of these numbers 25 5 11 and 23 52 7?
You can get hte greatest common factor of three numbers by the same method you use for two numbers: splitting each number into prime factors and taking all common factors. Or, if you want to use Euclid's algorithm: gcf(25, 5, 11) = gcf(gcf(25, 5), 11)). In other words, you can take the greatest common factor of any two numbers, then the greatest common factor of the result and the third number.
Why does the listing method always works to find the greatest common factor?
The greatest common factor of two numbers has to show up on the lists of factors of both numbers.
What is the greatest common factor of 18 and 20 using listing method?
It is: 2
What is the greatest common factor method of 132?
It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! There can, therefore, be no method for a question that has no meaning.
What is the greatest common factor of 46 168 and 280?
The highest common factor of 46 and 138 is 46Factorization method:46 = 2×23138 = 2×3×23highest common factor = 2×23 = 46Alternative (modular) method:138 mod 46 = 0so 46 is the highest common factor.
How do you find the greatest common factor of 210 and 308?
* One method is to factor each number into prime factors, and see what factors they have in common. 210 = 2x105 = 2x5x21 = 2x5x3x7, or 2x3x5x7. 308 = 2x154 = 2x2x77 = 2x2x7x11. The GCF is 2x7 = 14. * Another method (more efficient, especially for larger numbers) is Euclid's algorithm. In this case for example, the greatest common factor of 308 and 210 is the same as the greatest common factor of 210 and 98. This latter number is the remainder of the division of 308 by 210. Continue until one of the numbers is zero. In that case, the other one is the greatest common factor. 308/210 = 1, remainder 98 210/98 = 2, remainder 14 98/14 = 7, remainder 0. The previous remainder (14) is the GCF.
