Highest Common Factor of 694, 212, 567, 67 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 694, 212, 567, 67 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 694, 212, 567, 67 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 694, 212, 567, 67 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 694, 212, 567, 67 is 1.
HCF(694, 212, 567, 67) = 1
HCF of 694, 212, 567, 67 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 694, 212, 567, 67 is 1.
Highest Common Factor of 694,212,567,67 is 1
Step 1: Since 694 > 212, we apply the division lemma to 694 and 212, to get
694 = 212 x 3 + 58
Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 58 and 212, to get
212 = 58 x 3 + 38
Step 3: We consider the new divisor 58 and the new remainder 38, and apply the division lemma to get
58 = 38 x 1 + 20
We consider the new divisor 38 and the new remainder 20,and apply the division lemma to get
38 = 20 x 1 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 694 and 212 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(38,20) = HCF(58,38) = HCF(212,58) = HCF(694,212) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 567 > 2, we apply the division lemma to 567 and 2, to get
567 = 2 x 283 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 567 is 1
Notice that 1 = HCF(2,1) = HCF(567,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67 > 1, we apply the division lemma to 67 and 1, to get
67 = 1 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67 is 1
Notice that 1 = HCF(67,1) .
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Frequently Asked Questions on HCF of 694, 212, 567, 67 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 694, 212, 567, 67?
Answer: HCF of 694, 212, 567, 67 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 694, 212, 567, 67 using Euclid's Algorithm?
Answer: For arbitrary numbers 694, 212, 567, 67 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.