Highest Common Factor of 468, 774, 186 using Euclid's algorithm
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 468, 774, 186 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 468, 774, 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 468, 774, 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 468, 774, 186 is 6.
HCF(468, 774, 186) = 6
HCF of 468, 774, 186 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 468, 774, 186 is 6.
Highest Common Factor of 468,774,186 is 6
Step 1: Since 774 > 468, we apply the division lemma to 774 and 468, to get
774 = 468 x 1 + 306
Step 2: Since the reminder 468 ≠ 0, we apply division lemma to 306 and 468, to get
468 = 306 x 1 + 162
Step 3: We consider the new divisor 306 and the new remainder 162, and apply the division lemma to get
306 = 162 x 1 + 144
We consider the new divisor 162 and the new remainder 144,and apply the division lemma to get
162 = 144 x 1 + 18
We consider the new divisor 144 and the new remainder 18,and apply the division lemma to get
144 = 18 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 468 and 774 is 18
Notice that 18 = HCF(144,18) = HCF(162,144) = HCF(306,162) = HCF(468,306) = HCF(774,468) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 186 > 18, we apply the division lemma to 186 and 18, to get
186 = 18 x 10 + 6
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 186 is 6
Notice that 6 = HCF(18,6) = HCF(186,18) .
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Frequently Asked Questions on HCF of 468, 774, 186 using Euclid's Algorithm
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 468, 774, 186?
Answer: HCF of 468, 774, 186 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 468, 774, 186 using Euclid's Algorithm?
Answer: For arbitrary numbers 468, 774, 186 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.