The HCF of two numbers A and B is 26. The HCF of two other numbers C and D is 39. What is the HCF of A, B, C and D?

Options

A. 7
B. 13
C. 26
D. 28

Answer

To find the HCF of the four numbers A, B, C, and D, we can follow these steps:

### Step 1: Understand the HCF of A and B
Given that the HCF of A and B is 26, we can express A and B in terms of their factors:
- Let A = 26m (where m is an integer)
- Let B = 26n (where n is an integer)

### Step 2: Understand the HCF of C and D
Similarly, we are given that the HCF of C and D is 39. We can express C and D in terms of their factors:
- Let C = 39p (where p is an integer)
- Let D = 39q (where q is an integer)

### Step 3: Identify the common factors
Now, we need to find the HCF of A, B, C, and D. We have:
- A = 26m
- B = 26n
- C = 39p
- D = 39q

### Step 4: Factor the numbers
Next, we can break down the numbers into their prime factors:
- 26 can be factored into 2 × 13
- 39 can be factored into 3 × 13

### Step 5: Identify common prime factors
Now, we can see the common prime factors:
- The factor 13 is common in both 26 and 39.

### Step 6: Determine the HCF
Since 13 is the only common factor between A, B, C, and D, the HCF of A, B, C, and D is:
- HCF(A, B, C, D) = 13

### Conclusion
Thus, the HCF of the four numbers A, B, C, and D is **13**.

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