Highest Common Factor of 734, 7806 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, 7806 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 734, 7806 is 2 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, 7806 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, 7806 is 2.
HCF(734, 7806) = 2
HCF of 734, 7806 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, 7806 is 2.
Highest Common Factor of 734,7806 is 2
Step 1: Since 7806 > 734, we apply the division lemma to 7806 and 734, to get
7806 = 734 x 10 + 466
Step 2: Since the reminder 734 ≠ 0, we apply division lemma to 466 and 734, to get
734 = 466 x 1 + 268
Step 3: We consider the new divisor 466 and the new remainder 268, and apply the division lemma to get
466 = 268 x 1 + 198
We consider the new divisor 268 and the new remainder 198,and apply the division lemma to get
268 = 198 x 1 + 70
We consider the new divisor 198 and the new remainder 70,and apply the division lemma to get
198 = 70 x 2 + 58
We consider the new divisor 70 and the new remainder 58,and apply the division lemma to get
70 = 58 x 1 + 12
We consider the new divisor 58 and the new remainder 12,and apply the division lemma to get
58 = 12 x 4 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 734 and 7806 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(58,12) = HCF(70,58) = HCF(198,70) = HCF(268,198) = HCF(466,268) = HCF(734,466) = HCF(7806,734) .
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Frequently Asked Questions on HCF of 734, 7806 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, 7806?
Answer: HCF of 734, 7806 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 734, 7806 using Euclid's Algorithm?
Answer: For arbitrary numbers 734, 7806 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.