What are the simplest form of 88 and72

General
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what are the simplest form of 88 and72

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What are the simplest form of 88 and 72?

Answer: To find the simplest form of the fraction that represents the ratio of the numbers 88 and 72, you need to simplify the fraction \frac{88}{72} by finding the greatest common divisor (GCD) of both the numerator (88) and the denominator (72).

Step 1: Find the GCD of 88 and 72

To find the GCD, you can use different methods such as:

  1. Prime Factorization Method:

    • Prime factorize both numbers.
    • 88 factors into: (2^3 \times 11)
    • 72 factors into: (2^3 \times 3^2)

  2. Listing Factors Method:

    • List all the factors of each number and find the greatest common factor.
    • Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
    • Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

  3. Euclidean Algorithm:

    • Divide the larger number by the smaller number and take the remainder.
    • Repeat with smaller number and remainder until the remainder is 0.
    • 88 divided by 72 gives a remainder of 16.
    • 72 divided by 16 gives a remainder of 8.
    • 16 divided by 8 gives a remainder of 0.

From these methods, you can see that the GCD of 88 and 72 is 8.

Step 2: Simplify the Fraction

Using the GCD, you can simplify the original fraction by dividing both the numerator and the denominator by the GCD:

[
\frac{88 \div 8}{72 \div 8} = \frac{11}{9}
]

Conclusion

Therefore, the simplest form of the fraction \frac{88}{72} is \frac{11}{9}. This fraction is in its simplest form since 11 and 9 share no common divisors other than 1.

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