Highest Common Factor of 189, 634 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 189, 634 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 189, 634 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 189, 634 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 189, 634 is 1.
HCF(189, 634) = 1
HCF of 189, 634 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 189, 634 is 1.
Highest Common Factor of 189,634 is 1
Step 1: Since 634 > 189, we apply the division lemma to 634 and 189, to get
634 = 189 x 3 + 67
Step 2: Since the reminder 189 ≠ 0, we apply division lemma to 67 and 189, to get
189 = 67 x 2 + 55
Step 3: We consider the new divisor 67 and the new remainder 55, and apply the division lemma to get
67 = 55 x 1 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 189 and 634 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(67,55) = HCF(189,67) = HCF(634,189) .
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Frequently Asked Questions on HCF of 189, 634 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 189, 634?
Answer: HCF of 189, 634 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 189, 634 using Euclid's Algorithm?
Answer: For arbitrary numbers 189, 634 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.