Sum of two numbers is 16 and their HCF is 4. A denotes the greater of the two numbers, find the value of A.24812
Question
Sum of two numbers is 16 and their HCF is 4. A denotes the greater of the two numbers, find the value of A.24812
Solution
The problem states that the sum of two numbers is 16 and their highest common factor (HCF) is 4.
Let's denote the two numbers as A and B, where A is the greater number.
Since their HCF is 4, we can express the numbers as 4p and 4q, where p and q are co-prime numbers (i.e., their HCF is 1).
So, A + B = 16 becomes 4p + 4q = 16.
Dividing throughout by 4, we get p + q = 4.
Since p and q are co-prime and their sum is 4, the possible pairs (p, q) are (1, 3) and (3, 1).
But since A is the greater number, we take p = 3 and q = 1.
So, A = 4p = 4*3 = 12.
Therefore, the value of A is 12.
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