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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 is the GCF for 78 168 486?
To find the Greatest Common Factor (GCF) of 78, 168, and 486, we first need to find the prime factorization of each number. 78 = 2 * 3 * 13 168 = 2^3 * 3 * 7 486 = 2 * 3^5 Next, we identify the common prime factors among the three numbers, which are 2 and 3. The GCF is the product of these common prime factors raised to the lowest power they appear in any of the numbers. Therefore, the GCF of 78, 168, and 486 is 2 * 3 = 6.
