Greatest Common Factor basic Math test

32 FREE Math Ebook Downloads For Members

32 Free math ebooks

This quiz covers the topic of Greatest Common Factor or GCF(in short) of numbers. The underlying principle behind the GCF is that between any two or more given numbers, there always lies a common factor irrespective of what they are and the aim is to find that number which is largest among the common factors between those given numbers. Say for example two numbers 4 and 6. The common factors that they have are 1 and 2. Of the two numbers 1 and 2, 2 is larger hence the GCF of 4 and 6 is 2.This concept shall be used by the kid to solve the questions here and the quiz tries to give enough of the practice that is actually needed.

What is GCF and how to find it?

The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into all of those numbers. For example, the GCF of 12 and 18 is 6 because 6 is the largest number that divides evenly into both 12 and 18.

To find the GCF of two numbers, we can use the “divide and conquer” method. Start by dividing one of the numbers by the other. If there is no remainder, then the second number is a factor of the first number and is also a common factor. If there is a remainder, divide the second number by the remainder and continue dividing until you find a factor with no remainder. The largest of these factors is the GCF.

For example, let’s find the GCF of 12 and 18.

  • 12 / 18 = 0 remainder 12
  • 18 / 12 = 1 remainder 6
  • 12 / 6 = 2 remainder 0

Since 6 has no remainder when it divides into 12, it is a common factor of both numbers. And since it is the largest common factor, it is also the GCF.

We can also use prime factorization to find the GCF of two or more numbers. To do this, we first find the prime factorization of each number, which means breaking each number down into its prime factors (factors that are only divisible by 1 and itself). The GCF is the product of the common prime factors of all the numbers, each raised to the lowest exponent among all the numbers.

For example, let’s find the GCF of 12, 18, and 30.

  • The prime factorization of 12 is 2 x 2 x 3
  • The prime factorization of 18 is 2 x 3 x 3
  • The prime factorization of 30 is 2 x 3 x 5

The common prime factors are 2 and 3. The lowest exponent of 2 is 1 (in the factorization of 12), and the lowest exponent of 3 is 1 (also in the factorization of 12). So the GCF is 2 x 3 = 6.

The GCF is a useful concept in math because it helps us simplify fractions, find the least common multiple (LCM) of two or more numbers, and solve other math problems. It’s also important in everyday life, for example when we are trying to find the lowest common denominator of two or more fractions so we can add or subtract them.