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How do you prove that if the greatest common factor of A and B equals 1 and C does not equal 0 then the greatest common factor of AC and BC divides C?
If the greatest common factor/divisor of A and B is 1 then they are coprime - they do not share any prime factors. Multiplying both through by C means, obviously, that each number now divides by C. In fact, C is their greatest common divisor, since AC and BC do not have further common factors after C is taken out. Hence the GCF of AC and BC is not merely a factor of C - it is C. (The question makes sense only if A, B and C are integers.)
What is the greatest common factor of B and C?
Variables can have any value. That's an infinite number of factors.
What greatest common factor of 60 and C?
Since C can be any number, the answer can be any factor of 60.
What is the greatest common factor of A 60 B 105 and C 165?
The GCF of those numbers is 15.
A. 12 and 18 b. 2 and 4 c. 20 and 24 d. 12 and 24 What numbers have 6 as their greatest common factor?
A. 12 and 18
What is the greatest common factor of A B and C?
The GCF is 1.
What is the greatest common factor of the products ab ac and bc if b is a factor of c?
The answer depends on whether or not a is a factor of c.
How do you prove that if the greatest common factor of A and B equals 1 and C does not equal 0 then the greatest common factor of AC and BC divides C?
If the greatest common factor/divisor of A and B is 1 then they are coprime - they do not share any prime factors. Multiplying both through by C means, obviously, that each number now divides by C. In fact, C is their greatest common divisor, since AC and BC do not have further common factors after C is taken out. Hence the GCF of AC and BC is not merely a factor of C - it is C. (The question makes sense only if A, B and C are integers.)
What are the greatest common factors of 11 and 50?
the only common factor is 1 b/c 11 is a prime number.
What is the greatest common factor of A B C?
Variables can be any number, leaving an infinite number of GCF possibilities.
What is the greatest common factor of B and C?
Variables can have any value. That's an infinite number of factors.
Can the greatest common factor of 16 and 42 be greater than 16?
Well, think about what it means for something (say a number c) to be the greatest common factor of 2 numbers (say a and b *non-zero*).It means that c is the largest integer such that a and b are both divisible by c.If c > a, then how can a be divisible by c?If c > b, then how can b be divisible by c?Therefore c < a & bAs for 16 and 42:16 = 2 x 2 x 2 x 242 = 2 x 3 x 7The only shared (or common) prime factor is 2. Therefore the GCF is 2.Other answer:No, GCF(16,42) can't be greater than 16.GCF of two numbers a and b(where a>b) is always smaller than or equal to a.But why it can't be greater than a?GCF means greatest common factor, the greatest factor of a is a, and there can be many common factors of a and b. But a(factor of a) is the largest among all the common factors, so GCF can't be greater than a. Prime factorization of 16 = 2x2x2x2Prime factorization of 42 = 2x3x7What is common in the factorization of 16 and 42? Only 2 is common so GCF is 2.
Write a java program to find rational number in reduce form?
I assume numerator and denominator will be in two different variables, Just divide both of them by the greatest common factor.Here is a method to calculate the greatest common factor; it is based on the fact that, for example, the greatest common factor of 14 and 10 is the same as the greatest common factor of 10 and 4, where 4 is calculated as 14 - 10 (or faster, to avoid repeated subtractions, 14 % 10).public static void main(String[] args) {System.out.println(gcf(300L, 200L));}static long gcf(long a, long b){long c;while (true){c = a % b;if (c == 0) break;a = b;b = c;}return b;}
What does H C F mean in math?
GREATEST common factor
How do you do the divide out common factors?
Suppose you have a fraction in the form a/b and suppose c is a common factor of a and b.c is a factor of a so that a = c*xc is a factor of b so that b = c*ywhere x and y are integers.And so a/b = cx/cy = x/y.The process is as follows:find a common factor, c, of the numerator (a) and the denominator (b).the new numerator is the old numerator divided by the common factor that is, x = a/c;the new denominator is the old denominator divided by the common factor that is, y = b/c;the new fraction is x/y.
What greatest common factor of 60 and C?
Since C can be any number, the answer can be any factor of 60.
What is the greatest common factor of 81 181 and C?
That depends on the value of C.
