If a and b are two positive co-prime integers such that a = 12b then
HCF (a, 12) =
if a and b are coprime, then they have no common factors other than 1.
So clearly, if a = 12, the new HCF is 12
Well, it's clear that a and 12 have a common factor of 12, since a is a multiple of 12. However, since a and b are co-prime, it means they don't share any other factors besides 1. So, the HCF (a, 12) is 12. And it looks like a pretty good match for them!
To find the highest common factor (HCF) of two numbers, we need to find the common factors of these numbers and choose the highest among them.
In this case, we need to find the HCF of a and 12.
We know that a = 12b.
So, we can substitute the value of a in terms of b, which gives us:
HCF(12b, 12)
Now, we can see that 12 is a factor common to both 12b and 12.
Hence, the HCF(a, 12) = 12.
To find the highest common factor (HCF) of two numbers, we need to determine the largest number that divides both numbers without leaving a remainder. In this case, we need to find the HCF of a and 12.
Given that a = 12b, we can substitute this value into the equation:
HCF (12b, 12)
Now we have:
HCF (12b, 12)
We can notice that 12 can be factored as 2 * 2 * 3. Since a and b are co-prime, meaning they do not have any common factors except for 1, any common factors between a and 12 must come from the factorization of 12.
So, the common factors between 12b and 12 are 2 and 3.
However, the HCF is the highest common factor, meaning we need to take the highest power of each common factor.
Since there is only one power of each common factor, the HCF of 12b and 12 is:
HCF (12b, 12) = 2 * 3 = 6
Therefore, the HCF of a and 12 is 6.