Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 780, 204, 186 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 204, 186 is 6 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 780, 204, 186 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 780, 204, 186 is 6.
HCF(780, 204, 186) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 204, 186 is 6.
Step 1: Since 780 > 204, we apply the division lemma to 780 and 204, to get
780 = 204 x 3 + 168
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 168 and 204, to get
204 = 168 x 1 + 36
Step 3: We consider the new divisor 168 and the new remainder 36, and apply the division lemma to get
168 = 36 x 4 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 780 and 204 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(168,36) = HCF(204,168) = HCF(780,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 186 > 12, we apply the division lemma to 186 and 12, to get
186 = 12 x 15 + 6
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 12 and 186 is 6
Notice that 6 = HCF(12,6) = HCF(186,12) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 780, 204, 186?
Answer: HCF of 780, 204, 186 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 204, 186 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 204, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.