H.C.F of 1485 and 4356 is-

Options

A. 189
B. 89
C. 99
D. 83

Answer

To find the H.C.F (Highest Common Factor) of 1485 and 4356, we can use the prime factorization method. Here’s a step-by-step solution:

### Step 1: Prime Factorization of 1485
1. Start dividing 1485 by the smallest prime number, which is 3.
- 1485 ÷ 3 = 495
2. Divide 495 by 3 again.
- 495 ÷ 3 = 165
3. Divide 165 by 3 again.
- 165 ÷ 3 = 55
4. Now, divide 55 by the next prime number, which is 5.
- 55 ÷ 5 = 11
5. Finally, 11 is a prime number itself.

So, the prime factorization of 1485 is:
\[ 1485 = 3^3 \times 5^1 \times 11^1 \]

### Step 2: Prime Factorization of 4356
1. Start dividing 4356 by the smallest prime number, which is 2.
- 4356 ÷ 2 = 2178
2. Divide 2178 by 2 again.
- 2178 ÷ 2 = 1089
3. Now, divide 1089 by the next prime number, which is 3.
- 1089 ÷ 3 = 363
4. Divide 363 by 3 again.
- 363 ÷ 3 = 121
5. Finally, divide 121 by the next prime number, which is 11.
- 121 ÷ 11 = 11
6. And 11 is a prime number itself.

So, the prime factorization of 4356 is:
\[ 4356 = 2^2 \times 3^2 \times 11^2 \]

### Step 3: Finding the H.C.F
Now, we will find the H.C.F by taking the lowest power of all common prime factors:
- The common prime factors of 1485 and 4356 are 3 and 11.
- For 3, the minimum power is \(3^2\) (from 4356).
- For 11, the minimum power is \(11^1\) (from both).

Thus, the H.C.F is:
\[ H.C.F = 3^2 \times 11^1 = 9 \times 11 = 99 \]

### Final Answer
The H.C.F of 1485 and 4356 is **99**.

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