33 72 simplified

elenas club

2 min read

·

12-02-2025

5

0

Share

The fraction 33/72 might look daunting at first, but simplifying it is easier than you think. Simplifying, or reducing, a fraction means finding an equivalent fraction where the numerator (top number) and the denominator (bottom number) are smaller, but the fraction represents the same value. This guide will walk you through the process step-by-step.

Understanding Fraction Simplification

Simplifying fractions is all about finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both the numerator and denominator evenly (without leaving a remainder). Once you find the GCD, you divide both the numerator and the denominator by it to get your simplified fraction.

How to Simplify 33/72

Let's simplify 33/72.

1. Find the Greatest Common Divisor (GCD):

Several methods exist to find the GCD. We'll use the prime factorization method:

• Prime Factorization of 33: 33 = 3 x 11
• Prime Factorization of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²

The common prime factor between 33 and 72 is 3. Therefore, the GCD is 3.

2. Divide the Numerator and Denominator by the GCD:

Divide both the numerator (33) and the denominator (72) by the GCD (3):

• 33 ÷ 3 = 11
• 72 ÷ 3 = 24

3. The Simplified Fraction:

The simplified fraction is 11/24. This fraction is equivalent to 33/72, but it's in its simplest form because 11 and 24 share no common factors other than 1.

Alternative Methods for Finding the GCD

While prime factorization is a reliable method, other techniques exist:

• Listing Factors: List all the factors of 33 (1, 3, 11, 33) and 72 (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72). Identify the largest number common to both lists (3).

• Euclidean Algorithm: This method involves repeated division. Divide the larger number (72) by the smaller number (33). The remainder becomes the new divisor, and the process repeats until the remainder is 0. The last non-zero remainder is the GCD.

72 ÷ 33 = 2 with a remainder of 6 33 ÷ 6 = 5 with a remainder of 3 6 ÷ 3 = 2 with a remainder of 0

The GCD is 3.

Practice Makes Perfect

Simplifying fractions takes practice. Try simplifying other fractions using these methods. The more you practice, the easier it will become to identify the GCD quickly and efficiently. Remember, the goal is to find the largest number that divides both the numerator and denominator without leaving a remainder. This will always lead you to the simplest form of the fraction.