GCF - **G**reatest **C**ommon **F**actor is also known as **G**reatest **C**ommon **D**ivisor (GCD) or **H**ighest **C**ommon **F**actor (HCF). This worksheet will help you to know about concept of GCF, GCD or HCF. The HCF of two or more than two numbers is the greatest number that divides each one of them exactly.

**HCF/ GCF by Factorization**

Express each one of the given numbers as the product of prime factors. The product of least powers of common prime factors gives GCF/ HCF.

**Example for GCF, HCF calculation:**

What is H.C.F. of 2^{3} x 3^{2} x 5 x 7^{4} , 2^{2} x 3^{5} x 5^{2} x 7^{3} , 2^{3} x 5^{3} x 7^{2} . You can get Factorization for any given number using Prime Factorization calculator.

The prime numbers common to given number are 2, 5 & 7.

Therefore H.C.F. = 2^2 x 5 x 7^2 = 980.

**Find HCF by Division Method:**

Suppose we have to find the HCF of two given numbers. Divide the largest number smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding divisor by the remainder last obtained as remainder. The last divisor is the required HCF Suppose we have to find the HCF of there numbers. Then, HCF of [(HCF or GCF of any two) & (the third number)] gives the HCF of three given numbers. Similarly the HCF of more than three numbers may be obtained.

**HCF, GCF division method Example:**

Find the H.C.F. of 513, 1134 and 1215.

1134) 1215 (1

1134

81) 1134 (14

81

324

324

X

Therefore H.C.F. of 1134 & 1215 is 81.

Therefore the required H.C.F. = H.C.F. of 513 & 81.

81) 513 (6

486

27) 81 (3

81

X

Therefore HCF of given numbers = 27

The above worksheet is a walk through to understand the concept of GCF, HCF, GCD and GCF for the given numbers. When you try this calculation on your own, use this

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