Highest Common Factor of 764, 2914 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 764, 2914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 764, 2914 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 764, 2914 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 764, 2914 is 2.
HCF(764, 2914) = 2
HCF of 764, 2914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 764, 2914 is 2.
Highest Common Factor of 764,2914 is 2
Step 1: Since 2914 > 764, we apply the division lemma to 2914 and 764, to get
2914 = 764 x 3 + 622
Step 2: Since the reminder 764 ≠ 0, we apply division lemma to 622 and 764, to get
764 = 622 x 1 + 142
Step 3: We consider the new divisor 622 and the new remainder 142, and apply the division lemma to get
622 = 142 x 4 + 54
We consider the new divisor 142 and the new remainder 54,and apply the division lemma to get
142 = 54 x 2 + 34
We consider the new divisor 54 and the new remainder 34,and apply the division lemma to get
54 = 34 x 1 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 764 and 2914 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(54,34) = HCF(142,54) = HCF(622,142) = HCF(764,622) = HCF(2914,764) .
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Frequently Asked Questions on HCF of 764, 2914 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 764, 2914?
Answer: HCF of 764, 2914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 764, 2914 using Euclid's Algorithm?
Answer: For arbitrary numbers 764, 2914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
