Greatest Common Factor Of 75 And 60

Example 5 Find common factors of 75, 60 and 210 Chapter 1 Class 6 from www.teachoo.com

Introduction

Greatest Common Factor (GCF) refers to the largest number that divides two or more numbers without leaving any remainder. In this article, we will explore how to determine the GCF of 75 and 60.

Prime Factorization Method

One of the methods to find the GCF of two numbers is the Prime Factorization Method. In this method, we need to find the prime factors of both numbers and then identify the common factors.

Prime Factors of 75

The prime factors of 75 are 3 and 5. We can find this by dividing 75 by the smallest prime number, which is 2. 75 divided by 2 is not a whole number, so we proceed to divide it by the next prime number, which is 3. 75 divided by 3 is 25. We can further divide 25 by 5 to get the prime factors of 75, which are 3 and 5.

Prime Factors of 60

The prime factors of 60 are 2, 3, and 5. We can find this by dividing 60 by the smallest prime number, which is 2. 60 divided by 2 is 30. We can further divide 30 by 2 to get 15. We can then divide 15 by 3 to get 5. Therefore, the prime factors of 60 are 2, 2, 3, and 5.

Identifying Common Factors

Once we have found the prime factors of both numbers, we can identify the common factors. In this case, the common factors of 75 and 60 are 3 and 5.

Determining the GCF

To determine the GCF, we need to multiply the common factors. In this case, the GCF of 75 and 60 is 3 x 5 = 15.

Conclusion

In conclusion, the Prime Factorization Method is an effective way to find the GCF of two numbers. By finding the prime factors of both numbers and identifying the common factors, we can determine the GCF. In the case of 75 and 60, the GCF is 15, which is the largest number that divides both 75 and 60 without leaving any remainder.