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348/52 as a fraction

348/52 as a fraction

2 min read 05-02-2025
348/52 as a fraction

Simplifying 348/52: A Step-by-Step Guide

Title Tag: Simplify 348/52: Fraction Reduction Guide

Meta Description: Learn how to simplify the fraction 348/52 to its lowest terms. This step-by-step guide provides a clear explanation and demonstrates the process of finding the greatest common divisor (GCD). Improve your fraction skills today!

H1: Simplifying the Fraction 348/52

The fraction 348/52 represents a ratio or part of a whole. To make this fraction easier to understand and use in calculations, we need to simplify it to its lowest terms. This means finding the greatest common divisor (GCD) of both the numerator (348) and the denominator (52) and dividing both by it.

H2: Finding the Greatest Common Divisor (GCD)

The GCD is the largest number that divides evenly into both 348 and 52. There are several ways to find the GCD. Let's use the prime factorization method:

  • Prime Factorization of 348: We break down 348 into its prime factors (numbers divisible only by 1 and themselves). 348 = 2 x 2 x 3 x 29 = 2² x 3 x 29

  • Prime Factorization of 52: Similarly, we find the prime factors of 52. 52 = 2 x 2 x 13 = 2² x 13

Now, we identify the common prime factors and their lowest powers: Both numbers share two factors of 2 (2²).

Therefore, the GCD of 348 and 52 is 2² = 4.

H2: Simplifying the Fraction

Now that we've found the GCD (4), we divide both the numerator and the denominator by 4:

348 ÷ 4 = 87 52 ÷ 4 = 13

Therefore, the simplified fraction is 87/13.

H2: Verifying the Result

We can verify our simplification by checking if 87 and 13 share any common factors other than 1. Since 87 = 3 x 29 and 13 is a prime number, they have no common factors other than 1, confirming that 87/13 is the simplified form.

H2: Alternative Method: Euclidean Algorithm

Another method to find the GCD is the Euclidean Algorithm. This iterative method is particularly useful for larger numbers:

  1. Divide the larger number (348) by the smaller number (52): 348 ÷ 52 = 6 with a remainder of 36.
  2. Replace the larger number with the smaller number (52) and the smaller number with the remainder (36): 52 ÷ 36 = 1 with a remainder of 16.
  3. Repeat the process: 36 ÷ 16 = 2 with a remainder of 4.
  4. Repeat again: 16 ÷ 4 = 4 with a remainder of 0.
  5. The last non-zero remainder (4) is the GCD.

This confirms our earlier finding that the GCD is 4. Dividing both the numerator and denominator by 4 again gives us 87/13.

H2: Conclusion

Simplifying fractions is essential for making them easier to understand and work with. By finding the greatest common divisor and dividing both the numerator and the denominator by it, we successfully simplified 348/52 to its simplest form: 87/13. Remember to always check your answer to ensure it's in its lowest terms. Using either prime factorization or the Euclidean algorithm, you can efficiently simplify any fraction.

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