Highest Common Factor of 2682, 8826, 37036 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 2682, 8826, 37036 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2682, 8826, 37036 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 2682, 8826, 37036 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 2682, 8826, 37036 is 2.
HCF(2682, 8826, 37036) = 2
HCF of 2682, 8826, 37036 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2682, 8826, 37036 is 2.
Highest Common Factor of 2682,8826,37036 is 2
Step 1: Since 8826 > 2682, we apply the division lemma to 8826 and 2682, to get
8826 = 2682 x 3 + 780
Step 2: Since the reminder 2682 ≠ 0, we apply division lemma to 780 and 2682, to get
2682 = 780 x 3 + 342
Step 3: We consider the new divisor 780 and the new remainder 342, and apply the division lemma to get
780 = 342 x 2 + 96
We consider the new divisor 342 and the new remainder 96,and apply the division lemma to get
342 = 96 x 3 + 54
We consider the new divisor 96 and the new remainder 54,and apply the division lemma to get
96 = 54 x 1 + 42
We consider the new divisor 54 and the new remainder 42,and apply the division lemma to get
54 = 42 x 1 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2682 and 8826 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(54,42) = HCF(96,54) = HCF(342,96) = HCF(780,342) = HCF(2682,780) = HCF(8826,2682) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 37036 > 6, we apply the division lemma to 37036 and 6, to get
37036 = 6 x 6172 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 37036 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(37036,6) .
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Frequently Asked Questions on HCF of 2682, 8826, 37036 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 2682, 8826, 37036?
Answer: HCF of 2682, 8826, 37036 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2682, 8826, 37036 using Euclid's Algorithm?
Answer: For arbitrary numbers 2682, 8826, 37036 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.