Highest Common Factor of 734, 6537, 1961 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 734, 6537, 1961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 734, 6537, 1961 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 734, 6537, 1961 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 734, 6537, 1961 is 1.
HCF(734, 6537, 1961) = 1
HCF of 734, 6537, 1961 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 734, 6537, 1961 is 1.
Highest Common Factor of 734,6537,1961 is 1
Step 1: Since 6537 > 734, we apply the division lemma to 6537 and 734, to get
6537 = 734 x 8 + 665
Step 2: Since the reminder 734 ≠ 0, we apply division lemma to 665 and 734, to get
734 = 665 x 1 + 69
Step 3: We consider the new divisor 665 and the new remainder 69, and apply the division lemma to get
665 = 69 x 9 + 44
We consider the new divisor 69 and the new remainder 44,and apply the division lemma to get
69 = 44 x 1 + 25
We consider the new divisor 44 and the new remainder 25,and apply the division lemma to get
44 = 25 x 1 + 19
We consider the new divisor 25 and the new remainder 19,and apply the division lemma to get
25 = 19 x 1 + 6
We consider the new divisor 19 and the new remainder 6,and apply the division lemma to get
19 = 6 x 3 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 734 and 6537 is 1
Notice that 1 = HCF(6,1) = HCF(19,6) = HCF(25,19) = HCF(44,25) = HCF(69,44) = HCF(665,69) = HCF(734,665) = HCF(6537,734) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1961 > 1, we apply the division lemma to 1961 and 1, to get
1961 = 1 x 1961 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1961 is 1
Notice that 1 = HCF(1961,1) .
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Frequently Asked Questions on HCF of 734, 6537, 1961 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 734, 6537, 1961?
Answer: HCF of 734, 6537, 1961 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 734, 6537, 1961 using Euclid's Algorithm?
Answer: For arbitrary numbers 734, 6537, 1961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.