Highest Common Factor of 231, 435, 778, 677 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 231, 435, 778, 677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 231, 435, 778, 677 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 231, 435, 778, 677 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 231, 435, 778, 677 is 1.
HCF(231, 435, 778, 677) = 1
HCF of 231, 435, 778, 677 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 231, 435, 778, 677 is 1.
Highest Common Factor of 231,435,778,677 is 1
Step 1: Since 435 > 231, we apply the division lemma to 435 and 231, to get
435 = 231 x 1 + 204
Step 2: Since the reminder 231 ≠ 0, we apply division lemma to 204 and 231, to get
231 = 204 x 1 + 27
Step 3: We consider the new divisor 204 and the new remainder 27, and apply the division lemma to get
204 = 27 x 7 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 231 and 435 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(204,27) = HCF(231,204) = HCF(435,231) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 778 > 3, we apply the division lemma to 778 and 3, to get
778 = 3 x 259 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 778 is 1
Notice that 1 = HCF(3,1) = HCF(778,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 677 > 1, we apply the division lemma to 677 and 1, to get
677 = 1 x 677 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 677 is 1
Notice that 1 = HCF(677,1) .
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Frequently Asked Questions on HCF of 231, 435, 778, 677 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 231, 435, 778, 677?
Answer: HCF of 231, 435, 778, 677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 231, 435, 778, 677 using Euclid's Algorithm?
Answer: For arbitrary numbers 231, 435, 778, 677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.