Highest Common Factor of 612, 359, 371 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 612, 359, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 359, 371 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 612, 359, 371 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 612, 359, 371 is 1.
HCF(612, 359, 371) = 1
HCF of 612, 359, 371 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 359, 371 is 1.
Highest Common Factor of 612,359,371 is 1
Step 1: Since 612 > 359, we apply the division lemma to 612 and 359, to get
612 = 359 x 1 + 253
Step 2: Since the reminder 359 ≠ 0, we apply division lemma to 253 and 359, to get
359 = 253 x 1 + 106
Step 3: We consider the new divisor 253 and the new remainder 106, and apply the division lemma to get
253 = 106 x 2 + 41
We consider the new divisor 106 and the new remainder 41,and apply the division lemma to get
106 = 41 x 2 + 24
We consider the new divisor 41 and the new remainder 24,and apply the division lemma to get
41 = 24 x 1 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 612 and 359 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(41,24) = HCF(106,41) = HCF(253,106) = HCF(359,253) = HCF(612,359) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 371 > 1, we apply the division lemma to 371 and 1, to get
371 = 1 x 371 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 371 is 1
Notice that 1 = HCF(371,1) .
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Frequently Asked Questions on HCF of 612, 359, 371 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 612, 359, 371?
Answer: HCF of 612, 359, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 359, 371 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 359, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.