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- GCD Calculator

This calculator computes Greatest Common Divisor (GCD) of two or more numbers using four different methods.

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examples

example 1:ex 1:

What is the Greatest Common Divisor (GCD) of 104 and 64?

example 2:ex 2:

Find GCD of 96, 144 and 192 using a repeated division.

example 3:ex 3:

Find GCD of 54 and 60 using an Euclidean Algorithm.

example 4:ex 4:

Find GCD of 72 and 54 by listing out the factors.

This calculator uses four methods to find GCD. We will show them using an examples.

Example: find GCD of 36 and 48

Step 1: find prime factorization of each number:

42 = 2 * 3 * 7

70 = 2 * 5 * 7

Step 2: circle out all common factors:

42 = ② * 3 * ⑦

70 = ② * 5 * ⑦

We see that the GCD is ② * ⑦ = **14**

Example: find GCD of 84 and 140.

Step 1: Place the numbers inside division bar:

84 | 140 |

Step 2: Divide both numbers by 2:

2 |
84 | 140 |

42 |
70 |

Step 3: Continue to divide until the numbers do not have a common factor.

② | 84 | 140 |

② | 42 | 70 |

⑦ | 21 | 35 |

3 | 7 |

Step 4: The GCD of 84 and 140 is:
② * ② * ⑦ = **28**

Example: Find GCD of 52 and 36, using Euclidean algorithm.

Solution: Divide 52 by 36 and get the reminder, than divide 36 with the reminder from previous step. When the reminder is zero the GCD is the last divisor.

52 | : | 36 | = | 1 | reminder (16) | ||||

36 | : | 16 | = | 1 | reminder (4) | ||||

16 | : | ④ | = | 4 | reminder (0) |

We conclude that the GCD = 4.

Example: find GCD of 45 and 54 by listing out the factors.

Step 1: Find all divisors of the given numbers:

The divisors of 45 are 1, 3, 5, ⑨, 15 and 45

The divisors of 54 are 1, 2, 3, 6, ⑨ 18, 27 and 54

Step 2: The greatest divisor = ⑨

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