Greatest common factors

Let Us Learn About Greatest Common Factors

The Greatest Common Factor (GCF) is the largest number that is a common factor of two or more numbers.

How to find the greatest common factor:

· Determine if there is a common factor of the numbers. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.

· Divide all of the numbers by this common factor.

· Repeat this process with the resulting numbers until there are no more common factors.

· Multiply all of the common factors together to find the Greatest Common Factor

Greatest Common Factor is highest quantity that divides exactly into two or more Quantities. Finding the greatest common factor is listing the prime factors, and then multiplying the common prime factors. Find all the factors of two or more quantities, and find some factors are the same ("common"), and then the largest of those common factors is the Greatest Common Factor.

"GCF" is also called "Highest Common Factor". GCF is the "greatest" thing for simplifying fractions. It is simply the largest of the common factors two or more numbers. In this article we shall discuss about greatest common factor Study.

Study on Finding the Factors

GCF is made up of three words becomes

• Greatest (largest)
• Common(shared)
• Factor.( Factored Piece)

Factor:

Factors are the numbers multiplying together to get another number.

The factors of 14 are 1, 2,7 and 14...

Because 2 × 7 = 14, or 7 x 2 = 14, or 1 × 14 = 14.

Consider the numbers 12 and 30.

The factors of 12 are 1, 2, 3, 4, 6, and 12

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

So we get the common factors are 1, 2, 3, and 6.

Among these 1, 2, 3, and 6 the number 6 is the greatest.

So 6 is called as greatest common factor of 12 and 30.

Greatest common factor of two or more numbers is a common factor of the numbers which is greater among all the common factors.

Greatest Common Divisor (GCD) is also known as Highest Common Factor (HCF) or Greatest Common Measure (GCM).

Steps :

1.Find all the factors of each given number.

2.Find common factors of the given number.

3.The greatest of all the factors obtained in (Step 2) is the required G.C.D.

For example :

1)Greatest common factor of 18, 24 and 36.

Step 1, Find all the factors of each given number i.e. 18, 24 and 36.

Factors of 18 = 1, 2, 3, 6, 9 and 18,

factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

and factors of 36 = 1, 2, 3, 4, 6, 9,12, 18 and 36.

Step 2, [observe the common factors of the given number which are underlined].

Therefore, the common factors of 18, 24 and 36 = 1, 2, 3 and 6.

Step 3, [now observe the greatest of all the factors obtained in (Step 2) is the required G.C.D].

Therefore, Greatest common factor of 18, 24 and 36 = 6.

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