Tag: greatest common factor

The Geometric Representation of Greatest Common Factor

Elementary School Number Theory, High School Mathematics

A factor is an integer that divides another integer. The number 6 is a factor of 12 since 6 divides 12. It is easy to see that 1, 2, 3, 4, and 12 are also factors of 12. Looking at the numbers in the tables below, we can see that some numbers have only 2 factors, 1 and itself. These numbers are called prime numbers.

Two or more numbers can have common factors. For example, let us consider the factors of 12 and 18.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18  » Read more

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Euclidean Algorithm Explained for Elementary School

High School Mathematics, High School Number Theory

In number theory, the Euclidean algorithm is a method for getting the greatest common factor (GCF) or highest common factor (HCF) of two positive integers. It is usually used for larger numbers since prime factorization can be used to get the greatest common factor of small numbers. Many students are confused with this method, but if you look at it closely, even elementary students can actually do it.

Let us start with an example. Note that in the discussion below, we will use the terms dividend and divisor. In the division a ÷ b, a is the dividend and b is the divisor.  » Read more

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