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Yes the GCF is 1, and the numbers are called relatively prime.
One way to see this is to use the method of writing number in the prime factored form.
Then to find the GCF we look at the primes that two numbers in factored form have in common. We take the common primes which will be the ones with the smallest exponent.
For example, if one number contains a 22 and another a 25 the 22 is the common prime raise to the lower power. If we took the one raised to the higher power, it would not be common to both numbers
Now if both prime factorizations have no common factors then we could look at any and all primes p, as p0 which equals 1. Or we could simply say the only common factor is 1 since none of the primes are common.
Either way, 1 is the GCF and the numbers, weather prime or composite, are called relatively prime. We often use this notation for the GCF of 2 numbers a and b, (a,b) and in this case
(a,b)=1. Don't confuse this with ordered pairs.
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What is the GCF of 154 and 42?
The greatest common factor (GCF) is the largest factor that two or more numbers have in common. You find the GCF by listing the prime factors of each number. Find the prime factors the numbers have in common and multiply them.154: 2 x 7 x 1142: 2 x 3 x 7The factors they have in common are: 2 x 7GCF = 14
What is the greatest common factor of 140 and 252?
To find the GCF of two numbers, you first need to break them down into their prime factors. For 140 and 252, these are: 140 = 2x2x5x7 252 = 2x2x3x3x7 The next step is to identify common prime factors. In this case, both numbers have two 2s and a 7 in their prime factors. To find the GCF, we simply multiply these common prime factors together: 2x2x7 = 28. Thus the greatest common factor of 140 and 252 is 28.
What is the GCF of 32 40 and 64?
To find the GCF of 3 numbers you first need to write them as their prime factors: 32 = 2x2x2x2x2 40 = 2x2x2x5 64 = 2x2x2x2x2x2 The next step is to identify any common factors. In this case, all three numbers have three 2s as prime factors. Multiply these together to find the GCF: 2x2x2 = 8 Thus the GCF of 32, 40 and 64 is 8.
How is the greatest common factor of two numbers found if you know the prime common to the numbers?
If there's only one prime common to the numbers, that's the GCF. If there's more than one, multiply them together. That's the GCF.
What does it mean if two numbers are relatively prime?
Two numbers are relatively prime if they have no factors in common other than 1. This means their greatest common factor (GCF) is 1. Here are examples of pairs of numbers that are relatively prime: 2, 9 5, 14 13, 998 3, 379 37, 303 691, 701 32, 81 384, 625 Here are examples of pairs of numbers that are not relatively prime: 2, 8 (GCF: 2) 16, 1060 (GCF: 4) 52, 117 (GCF: 13)
How can you determine whether the gcf of two numbers is one by looking at their prime factorizations?
If there are no prime factors in common, the GCF is 1.
How can you find the gcf of two numbers is 1by looking at their prime factorazations?
If they have no prime factors in common, their GCF is 1.
If two numbers have no common prime factors is the GCF one?
Yes.
What is the co-prime numbers?
Two numbers are considered to be co-prime if they share no common prime factors, that is, if their GCF is 1.
What is the gcf of 751 and 1000?
The gcf is 1, they have no common factors. We call these numbers relatively prime.
What is the Greatest common factor of 545 and 1024?
To find the greatest common factor (GCF), first find the prime factorization of the two numbers. The GCF is the product of all of the prime factors the two numbers have in common. If two numbers have no common factors, the GCF is 1. (Since all numbers are divisible by 1.) Prime factors of 545: 5, 109 Prime factors of 1024: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 They have in common: Nothing. The GCF is 1.
Why do you only need the common prime factors when finding the greatest common factor?
All numbers (except 0 and 1) are either prime or composite. All composite numbers can be expressed as the product of prime factors. So the GCF will either be a single prime number or a combination of prime numbers. Of course, if there are no common prime numbers, the GCF is 1.
How do you figure greatest common factor?
To find the greatest common factor (GCF), first find the prime factorization of the two numbers. The GCF is the product of all of the prime factors the two numbers have in common. If two numbers have no common factors, the GCF is 1. (Since all numbers are divisible by 1.) Example: Find the GCF of 60 and 24. Prime factors of 60: 2, 2, 3, 5 Prime factors of 24: 2, 2, 2, 3 Common factors: 2, 2, 3 GCF: 2x2x3=12 Example: Find the GCF of 17 and 21. Prime factors of 17: 17 Prime factors of 21: 3, 7 Common factors: None (1). GCF: 1
what is the largest factor that two numbers share is called?
The greatest common factor (GCF) of two (or more) numbers is the greatest factor that divides two numbers. To find the GCF you must work out and list the prime factors of each of the numbers. You will see that the numbers have prime factors in common. Multiply those factors the numbers have in common together and this gives you the GCF for the numbers. eg Number A = 18, Prime factors = 2*3*3 Number B = 24, Prime factors = 2*2*2*3 The Prime factors that A and B have in common are 2 and 3 Multiply them together = 6 6= the GCF of 18 and 24
How can you tell by looking at the prime factorization of two whole numbers that their gcf is 1?
If the prime factors of the first whole number are all different from the prime factors of the second whole number, then the GCF is 1.
How can you determine if the least common multiple of 2 numbers is the product of the 2 numbers or less than the product of the 2 numbers?
If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.
What are relativley prime numbers?
Positive integers are considered relatively prime when their GCF is 1, that is, when they have no common prime factors.
