Highest Common Factor of 641, 814, 137 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 641, 814, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 641, 814, 137 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 641, 814, 137 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 641, 814, 137 is 1.
HCF(641, 814, 137) = 1
HCF of 641, 814, 137 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 641, 814, 137 is 1.
Highest Common Factor of 641,814,137 is 1
Step 1: Since 814 > 641, we apply the division lemma to 814 and 641, to get
814 = 641 x 1 + 173
Step 2: Since the reminder 641 ≠ 0, we apply division lemma to 173 and 641, to get
641 = 173 x 3 + 122
Step 3: We consider the new divisor 173 and the new remainder 122, and apply the division lemma to get
173 = 122 x 1 + 51
We consider the new divisor 122 and the new remainder 51,and apply the division lemma to get
122 = 51 x 2 + 20
We consider the new divisor 51 and the new remainder 20,and apply the division lemma to get
51 = 20 x 2 + 11
We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get
20 = 11 x 1 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 641 and 814 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(51,20) = HCF(122,51) = HCF(173,122) = HCF(641,173) = HCF(814,641) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 1, we apply the division lemma to 137 and 1, to get
137 = 1 x 137 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 137 is 1
Notice that 1 = HCF(137,1) .
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Frequently Asked Questions on HCF of 641, 814, 137 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 641, 814, 137?
Answer: HCF of 641, 814, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 641, 814, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 641, 814, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.