To find the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of the numbers 204, 1190, and 1445, follow these steps:
### Step 1: Find the HCF of 204 and 1190
First, we need to calculate the HCF of the two numbers, 204 and 1190.
- The prime factors of 204 are 2, 2, 3, and 17 (since [tex]\( 204 = 2^2 \times 3 \times 17 \)[/tex]).
- The prime factors of 1190 are 2, 5, 7, and 17 (since [tex]\( 1190 = 2 \times 5 \times 7 \times 17 \)[/tex]).
The common prime factors are 2 and 17.
Thus, the HCF of 204 and 1190 is [tex]\( 2 \times 17 = 34 \)[/tex].
### Step 2: Find the HCF of the result from Step 1 (34) and 1445
Next, we need to find the HCF of 34 and 1445.
- The prime factors of 34 are 2 and 17 (since [tex]\( 34 = 2 \times 17 \)[/tex]).
- The prime factors of 1445 are 5, 17, and 17 (since [tex]\( 1445 = 5 \times 17 \times 17 \)[/tex]).
The common prime factor is 17.
Thus, the HCF of 34 and 1445 is 17.
### Final Result:
Therefore, the HCF of 204, 1190, and 1445 is 17.
