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Enter up to 10 numbers to calculate Greatest Common Factor (GCF / HCF) using our GCF Calculator (HCF Calculator)

Table of Contents:

**If number ‘a’ divided another number ‘b’ exactly, then we say that ‘a’ is a factor of ‘b’.**

**In this case, ‘b’ is called a multiple of ‘a’.**

HCF or Highest Common Factor (a.k.a Greatest common factor) refers to a set of two or more different numbers that can be divided by exactly or a common number. HCF is also called as GCD/GCM – Greatest Common Divisor, Greatest common denominator, or Greatest Common Factor.

LCM or Least Common Multiple refers to the smallest quantity of number that is divisible by two or more given quantities of number without a remainder: 12is the least common multiple of 2, 3, 4, and 6. LCM is also called as Lowest Common Multiple. LCM is the smallest number that is multiple of two or more numbers.

GCF - Greatest common factor can be calculated by any of the following methods,

HCF Calculator uses following methods to find greatest common divisor:

- List of Factors Method
- Prime Factorization Method
- Division Method
- Euclidean Algorithm
- Binary (Stein's) Algorithm
- Upside Down Division

**How to Calculate HCF?**

In the above picture, the greatest common factor of 12 and 16 is found through the factorization method. Firstly, the all the factors of both the numbers are written and the largest number is considered as HCF.

This is another method of finding the greatest common factor of 30 and 42. Firstly, you have to divide the largest number by the smallest number in the first step.

In the second step, the divisor will become the new dividend and so in the next steps. Until the remainder becomes zero, continue the steps where the last divisor will be HCF. In the picture above, the last divisor is 6 when remainder is 0 and this divisor is the Greatest Common Factor.

In simple steps, you can use the Factor Tree method to find the greatest common factor of 24 and 36 as shown in the above picture.

Firstly, make the factors of both the number like it is made for 24 and 36 in above image. Then find the common factors in both the number, line for 24 and 36, the common factors are 2,2,3.

Later, multiple the common factors to get the GCF and if there’s only one common factor then no need to multiply.

__(Greatest common divisor) Division Method:__

To find the HCF of two given numbers use GCF calculator, or divide the largest by the small number, then divide the dividend by the remainder. Repeat this until remainder is 0. The last dividend is the HCF of the two numbers.

Least Commmon Factor(LCF) can be calculated by the following method,

__Factorization Method:__

Express each one of the numbers as product of prime factors.

The product of highest powers of all prime factors gives LCF.

__ Example__:

**Calculate the HCF (GCF or GCD) and LCM for the given set of numbers.**

Greatest Common Factor of 18,36,72

__ Solution__:

**Step1****:** Express the numbers as product of prime factors.

18 = 2× 3^{2}

36 = 2^{2} × 3^{2}

72 = 2^{3} × 3^{2}

**Step2****:** Take the prime numbers with least power and is present in all sets.

2 and 3 are the prime number common to all given numbers.

The least power of 2 in the set is - 2

The least power of 3 in the set is - 3^{2}

__ Step3:__ Product of the numbers taken.

3

Least Common Multiple or Factor of 36, 90, 72.

**Step1****:** Express the numbers as product of prime factors.

36 = 2^{2} × 3^{2}

90 = 2 × 5 × 3^{2}

72 = 2^{3} × 3^{2}

__ Step2:__ Take the prime numbers with highest power for all prime numbers.

2, 3,5 are the prime number identified.

The highest power of 2 in the set is - 2

The highest power of 3 in the set is - 3

The highest power of 5 in the set is - 5

3

So 360 is the LCM (Least Common Multiple) of the numbers.

HCF of 2 and 4 is | 2 |

HCF of 2 and 5 is | 1 |

HCF of 3 and 4 is | 1 |

HCF of 5 and 25 is | 5 |

HCF of 4 and 5 is | 1 |

HCF of 16 and 24 is | 8 |

HCF of 5 and 7 is | 1 |

HCF of 15 and 20 is | 20 |

HCF of 13,23 and 14 is | 1 |

H.C.F of 8,9 and 25 is | 1 |

HCF of 2 and 3 is | 1 |

HCF of 4 and 8 is | 4 |

HCF of 3,4 and 6 is | 1 |

HCF of 3 and 5 is | 1 |

HCF of 680,510 and 340 is | 4 |

HCF of 2 and 8 is | 2 |

HCF of 18 and 48 is | 6 |

HCF of 12 and 48 is | 12 |

HCF of 30 and 42 is | 6 |

**1-** https://www.purplemath.com/modules/lcm_gcf.htm

**2**- http://mathforum.org/library/drmath/sets/select/dm_lcm_gcf.html

**3- **https://www.analyzemath.com/middle_school_math/grade_7/gcf.html

**4**- https://www.math-only-math.com/highest-common-factor-of-monomials.html

**5- **https://www.chilimath.com/lessons/introductory-algebra/greatest-common-factor/