The Greatest Common Factor (Gcf) Of 36 And 84


Greatest Common Factor of 36 and 84 Calculatio
Greatest Common Factor of 36 and 84 Calculatio from calculat.io

What is GCF?

The Greatest Common Factor or GCF is the largest number that divides two or more integers without leaving a remainder. It is also known as the Greatest Common Divisor or Highest Common Factor.

How to find the GCF?

There are several methods to find the GCF of two or more numbers. One method is to list down all the factors of each number and find the common factors. Then, select the largest common factor as the GCF. Another method is to use prime factorization, which involves breaking down the numbers into their prime factors and finding the common factors.

The Factors of 36 and 84

To find the GCF of 36 and 84, we need to list down all their factors. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

The Common Factors of 36 and 84

To find the common factors of 36 and 84, we need to look for the numbers that appear in both lists. The common factors of 36 and 84 are 1, 2, 3, 4, 6, and 12.

The GCF of 36 and 84

To find the GCF of 36 and 84, we need to select the largest common factor, which is 12. Therefore, the GCF of 36 and 84 is 12.

Why is GCF important?

The GCF is important in many mathematical operations, such as simplifying fractions, finding equivalent fractions, and solving equations. It can also be used to find the least common multiple (LCM) of two or more numbers.

How to check if 12 is the GCF?

To check if 12 is the GCF of 36 and 84, we need to divide both numbers by 12. If the result is a whole number, then 12 is a common factor. If not, then 12 is not a common factor. 36 ÷ 12 = 3 and 84 ÷ 12 = 7. Therefore, 12 is not a common factor of 36 and 84.

What is the correct GCF?

Since 12 is not a common factor of 36 and 84, we need to look for the next largest common factor. The next largest common factor is 6. Therefore, the GCF of 36 and 84 is 6.

Conclusion

In conclusion, the GCF of 36 and 84 is 6. To find the GCF, we need to list down all the factors of each number and find the common factors. Then, select the largest common factor as the GCF. The GCF is important in many mathematical operations, and it can be used to find the least common multiple of two or more numbers.

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