Finding the greatest common factor (GCF) or HCF of two numbers is an essential math skill based on determining the factors of a number. The topic of GCF holds great importance in school math as well as in math of higher grades. This concept is applied in number theory, fractions, modular arithmetic, and many other math topics. The sound knowledge of this topic’s fundamental concepts is foundational for advanced math taught in the later grades.
A child learns the concept of factors and multiple in lower classes. Proceeding to higher grades, they study more complex concepts based on them. Kids start to learn the concept of LCM, GCF, or HCF and various word problems based on them. To understand the concept of HCF, a child needs to have a clear understanding of factorization. The knowledge of GCF is also valuable for simpler applications like simplifying fractions. For this reason, it is vital that the child understands and learns the concept of factors and GCF from the beginning to master various skills based on it.
What is GCF?
In the language of basic algebra, the greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers have the same in a given set. This factor should divide all the numbers without any remainder.
The process of finding GCF mainly includes factorization of given numbers into factors. It is also known as the highest common factor(HCF) or highest common divisor(HCD). Understanding the concept of GCF requires the knowledge of factors and common factors of numbers.
Factors & Common Factors:
Factors of any number are the numbers that, on multiplying, produce back the number. Common factors of any two given numbers are the numbers that divide those numbers completely. For example: To find the greatest common factor of 6 and 12, list all the factors of 6 & 12 and select the greatest value, i.e., 6. All the factors of 6 are 1, 2, 3, 4 and 6. The factors of 12 are 1, 2, 3, 4, 6 and 12. Therefore, the common factors of 6 and 12 are 1, 2, 3, 4 and 6.
Methods to find the GCF:
There are various methods involved in finding the GCF of a set of given numbers:
- Listing the factors Method.
- Prime Factorization Method.
- Division Method
Listing the factors Method:
This Method of finding GCF includes listing all the factors of any given number and then finding the highest common factor among them. Steps of listing the factors method:
- Write a list of all the factors of each number.
- Mark all the common factors.
- Find the common factor with the greatest value.
Prime Factorization Method:
The prime factorization method includes representing a number as a product of all its prime factors, starting from that number’s smallest prime factor. Steps of prime factorization method:
- Write all the prime factors of any given set of numbers.
- Mark all the common factors among the factors of numbers.
- Multiply the common factors found in each number, and this number is the greatest common factor of the set of numbers.
This division method of grouping objects in equal groups is applicable to find the GCF of small numbers. Follow the long division method for large numbers, which breaks down a division problem into a series of easier steps.
Children usually depend on memorizing various mathematical concepts despite understanding them. This type of learning leads to poor subject knowledge and a lack of interest in the topic. When children learn math through reasoning and logic, they gain conceptual fluency. Cuemath helps kids to understand math logically by strengthening their reasoning skills. Sound conceptual knowledge of each topic allows children to develop connections between various math topics, forming a strong math foundation.