Highest Common Factor of 194, 321 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 194, 321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 194, 321 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 194, 321 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 194, 321 is 1.
HCF(194, 321) = 1
HCF of 194, 321 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 194, 321 is 1.
Highest Common Factor of 194,321 is 1
Step 1: Since 321 > 194, we apply the division lemma to 321 and 194, to get
321 = 194 x 1 + 127
Step 2: Since the reminder 194 ≠ 0, we apply division lemma to 127 and 194, to get
194 = 127 x 1 + 67
Step 3: We consider the new divisor 127 and the new remainder 67, and apply the division lemma to get
127 = 67 x 1 + 60
We consider the new divisor 67 and the new remainder 60,and apply the division lemma to get
67 = 60 x 1 + 7
We consider the new divisor 60 and the new remainder 7,and apply the division lemma to get
60 = 7 x 8 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 194 and 321 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(60,7) = HCF(67,60) = HCF(127,67) = HCF(194,127) = HCF(321,194) .
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Frequently Asked Questions on HCF of 194, 321 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 194, 321?
Answer: HCF of 194, 321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 194, 321 using Euclid's Algorithm?
Answer: For arbitrary numbers 194, 321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.