To find the highest common factor (HCF) of the numbers 131313, 232323, 333333, and 434343, we can follow these steps:

Step 1: Prime Factorization

We need to find the prime factorization of each of the given numbers.

1. 131313:

   • 131313 = 3 × 7 × 11 × 13 × 43

2. 232323:

   • 232323 = 3 × 7 × 11 × 17 × 43

3. 333333:

   • 333333 = 3 × 7 × 11 × 13 × 37

4. 434343:

   • 434343 = 3 × 7 × 11 × 13 × 43

Step 2: Identify Common Factors

Now, we look for the common factors in all the factorizations:

• 3
• 7
• 11

Step 3: Multiply the Common Factors

The highest common factor (HCF) is the product of the common prime factors.

$\text{HCF} = 3 \times 7 \times 11 = 231$

So, the highest common factor of 131313, 232323, 333333, and 434343 is 231.

Would you like more details or have any questions?

Related Questions:

1. What is the least common multiple (LCM) of these four numbers?
2. How do you find the HCF using the Euclidean algorithm?
3. Can the HCF of two numbers ever be greater than either of the numbers?
4. What is the difference between HCF and GCD (Greatest Common Divisor)?
5. How does prime factorization help in finding the HCF?

Tip:

When finding the HCF, always ensure that you identify all common factors, including the smallest primes, as they play a crucial role in determining the correct result.