let d be the HCF of 24 and 36 . find two no.s and b such that d = 24a + 36b
maths
To find two numbers a and b such that the highest common factor (HCF) of 24 and 36, represented by d, is equal to 24a + 36b, you can use the Euclidean algorithm for finding the HCF of two numbers.
First, let's find the HCF of 24 and 36 using the Euclidean algorithm:
Step 1: Divide 36 by 24: 36 ÷ 24 = 1, remainder 12
Step 2: Divide 24 by 12: 24 ÷ 12 = 2, remainder 0
Since the remainder is 0, this means that 12 is the HCF of 24 and 36.
Now, let's express 12 as 24a + 36b:
12 = 24a + 36b
Divide the equation by 12 to simplify it:
12/12 = (24a + 36b)/12
1 = 2a + 3b
Since we need to find two numbers a and b, we can assign values to one of the variables and solve for the other.
Let's assign a = 3:
1 = 2(3) + 3b
1 = 6 + 3b
3b = 1 - 6
3b = -5
b = -5/3
Therefore, the values of a and b that satisfy the equation are a = 3 and b = -5/3, and the HCF of 24 and 36 is equal to 24(3) + 36(-5/3).