Highest Common Factor of 774, 210, 181 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 774, 210, 181 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 210, 181 is 1 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 774, 210, 181 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 774, 210, 181 is 1.
HCF(774, 210, 181) = 1
HCF of 774, 210, 181 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 210, 181 is 1.
Highest Common Factor of 774,210,181 is 1
Step 1: Since 774 > 210, we apply the division lemma to 774 and 210, to get
774 = 210 x 3 + 144
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 144 and 210, to get
210 = 144 x 1 + 66
Step 3: We consider the new divisor 144 and the new remainder 66, and apply the division lemma to get
144 = 66 x 2 + 12
We consider the new divisor 66 and the new remainder 12,and apply the division lemma to get
66 = 12 x 5 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma 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 774 and 210 is 6
Notice that 6 = HCF(12,6) = HCF(66,12) = HCF(144,66) = HCF(210,144) = HCF(774,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 181 > 6, we apply the division lemma to 181 and 6, to get
181 = 6 x 30 + 1
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 1 and 6, to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 181 is 1
Notice that 1 = HCF(6,1) = HCF(181,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 774, 210, 181 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 774, 210, 181?
Answer: HCF of 774, 210, 181 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 210, 181 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 210, 181 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.