This calculator computes Greatest Common Divisor (GCD) of two or more numbers using four different methods.
This calculator uses four methods to find GCD. We will show them using few 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 remainder, then divide 36 with the remainder from previous step. When the remainder is zero the GCD is the last divisor.
52 | : | 36 | = | 1 | remainder (16) | ||||
36 | : | 16 | = | 1 | remainder (4) | ||||
16 | : | ④ | = | 4 | remainder (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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