What are the simpleest form of 88 and72

General
1

what are the simpleest form of 88 and72

2

What is the simplest form of 88 and 72?

Answer:

To find the simplest form of a fraction, you need to simplify it by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, we are trying to simplify the fraction 88/72.

Step 1: Find the Greatest Common Divisor (GCD)

  1. Prime Factorization:

    • Find the prime factors of 88.

      • 88 is even, divide by 2: 88 \div 2 = 44
      • 44 is even, divide by 2: 44 \div 2 = 22
      • 22 is even, divide by 2: 22 \div 2 = 11
      • 11 is a prime number, so the prime factorization of 88 is: 2^3 \times 11

    • Find the prime factors of 72.

      • 72 is even, divide by 2: 72 \div 2 = 36
      • 36 is even, divide by 2: 36 \div 2 = 18
      • 18 is even, divide by 2: 18 \div 2 = 9
      • 9 is divisible by 3, divide by 3: 9 \div 3 = 3
      • 3 is a prime number, so the prime factorization of 72 is: 2^3 \times 3^2

  2. Identify the Common Factors:

    • The prime factorization of both numbers includes 2^3.
    • Therefore, the greatest common divisor (GCD) is 2^3 = 8.

Step 2: Simplify the Fraction

  1. Divide Both Numbers by the GCD:

    • Divide the numerator (88) by 8: 88 \div 8 = 11
    • Divide the denominator (72) by 8: 72 \div 8 = 9

  2. Resulting Simplified Fraction:

    • The fraction 88/72 simplifies to 11/9.

Final Answer:

The simplest form of the fraction 88/72 is 11/9.