HCF

Summary

In this scenario, two farmers, Ramesh and Suresh, each own fields measuring 120 acres and 180 acres, respectively. They aim to divide their land into equal-sized plots with the largest possible area. The question revolves around finding the greatest common divisor (GCD) of their land areas, which would determine the largest plot size they could both use. The GCD of 120 and 180 is 60 acres, but this option isn't listed among the choices, so the correct answer is 'Not available.'

Takeaways

• 😀 Two farmers, Ramesh and Suresh, each own fields with different acreages.
• 😀 Ramesh's field is 120 acres in size.
• 😀 Suresh's field is 180 acres in size.
• 😀 Both farmers want to divide their land into equal-sized plots.
• 😀 The goal is to make each plot as large as possible.
• 😀 The problem asks for the largest possible area of each plot that can divide both fields equally.
• 😀 The options for the area of each plot are 10 acres, 20 acres, 30 acres, 40 acres, or 'not available'.
• 😀 To find the largest plot size, we need to calculate the greatest common factor (GCF) of 120 and 180.
• 😀 The GCF of 120 and 180 is 60.
• 😀 The largest possible area of each plot, based on the GCF, is 60 acres.

Q & A

What is the problem described in the script?

The script describes a problem where two farmers, Ramesh and Suresh, own fields of 120 acres and 180 acres, respectively. They want to divide their land into equal-sized plots with the largest possible area.

What is the main goal of Ramesh and Suresh?

The main goal is to divide their land into equal-sized plots such that each plot has the maximum possible area.

How do you find the maximum area of each plot that can divide both lands evenly?

To find the maximum area, you need to calculate the greatest common factor (GCF) or highest common divisor (HCD) of the two areas (120 acres and 180 acres).

What is the formula to calculate the GCF of two numbers?

The GCF of two numbers is found by determining the prime factorization of both numbers and selecting the lowest power of each common prime factor.

What is the prime factorization of 120?

The prime factorization of 120 is 2^3 * 3 * 5.

What is the prime factorization of 180?

The prime factorization of 180 is 2^2 * 3^2 * 5.

What is the GCF of 120 and 180?

The GCF of 120 and 180 is 60 acres, as it is the product of the lowest powers of common prime factors: 2^2 * 3 * 5.

What are the possible plot sizes listed in the multiple-choice options?

The multiple-choice options for plot sizes are: A) 10 acres, B) 20 acres, C) 30 acres, D) 40 acres, and E) Not available.

Why is the correct answer not listed in the multiple-choice options?

The largest possible plot size, which is the GCF of 120 and 180 acres, is 60 acres. Since 60 acres is not one of the options, the correct answer is 'E. Not available.'

What is the importance of calculating the GCF in this scenario?

Calculating the GCF is crucial because it ensures that the land can be divided into the largest possible equal-sized plots, maximizing the use of both fields while maintaining equal division.