The greatest common factor (GCF) of two numbers is the largest number that divides both of them evenly. It is a useful tool for simplifying fractions and solving mathematical problems. Knowing how to calculate the GCF is an important part of mathematics and can be used in a variety of contexts. In this article, we will look at the GCF of 4xy2 and 20x2y4.

## What is the Greatest Common Factor?

The greatest common factor (GCF) of two numbers is the largest number that divides both of them evenly. It is also known as the highest common factor (HCF) or the greatest common divisor (GCD). For example, the GCF of 12 and 18 is 6, because 6 is the largest number that divides them both evenly.

## Factors of 4xy2

The factors of 4xy2 are 1, 2, 4, x, y, xy, 2x, 2y, and 4xy.

## Factors of 20x2y4

The factors of 20x2y4 are 1, 2, 4, 5, 10, x, y, xy, 2x, 2y, 4x, 4y, 5x, 5y, 10x, 10y, 2xy, 4xy, and 20x2y4.

## Greatest Common Factor Calculation

To calculate the GCF of two numbers, first list their factors and then identify the common factors. The GCF is the largest number that appears on both lists.

## Analyzing the GCF

The GCF is a useful tool for simplifying fractions, solving equations, and finding the least common multiple of two numbers. It can also be used to determine whether two numbers are relatively prime or not.

## What is the GCF of 4xy2 and 20x2y4?

The GCF of 4xy2 and 20x2y4 is 4xy.

## Exploring Prime Factorization

The prime factorization of a number is the list of prime numbers that multiply together to create the original number. Prime numbers are those which can only be divided by 1 and themselves.

## Prime Factors of 4xy2

The prime factors of 4xy2 are 2, x, and y.

## Prime Factors of 20x2y4

The prime factors of 20x2y4 are 2, 5, x, and y.

## Common Prime Factors

The common prime factors of 4xy2 and 20x2y4 are 2 and y.

## Calculating the GCF

To calculate the GCF of 4xy2 and 20x2y4, we multiply the common prime factors together. In this case, the GCF is 2 x y = 4xy.

## Result of GCF Calculation

The result of the GCF calculation is 4xy.

## Conclusion

The GCF of 4xy2 and 20x2y4 is 4xy. To calculate the GCF of two numbers, list their factors and identify the common factors. The GCF is the largest number that appears on both lists. Prime factorization can also be used to find the GCF, by multiplying the common prime factors together. Knowing how to calculate the GCF is an important part of mathematics and can be used in a variety of contexts.

In conclusion, the greatest common factor of 4xy2 and 20x2y4 is 4xy. Knowing how to calculate the GCF is an important part of mathematics and can be used in a variety of contexts.