Highest Common Factor of 3624, 1682 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 3624, 1682 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3624, 1682 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 3624, 1682 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 3624, 1682 is 2.
HCF(3624, 1682) = 2
HCF of 3624, 1682 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3624, 1682 is 2.
Highest Common Factor of 3624,1682 is 2
Step 1: Since 3624 > 1682, we apply the division lemma to 3624 and 1682, to get
3624 = 1682 x 2 + 260
Step 2: Since the reminder 1682 ≠ 0, we apply division lemma to 260 and 1682, to get
1682 = 260 x 6 + 122
Step 3: We consider the new divisor 260 and the new remainder 122, and apply the division lemma to get
260 = 122 x 2 + 16
We consider the new divisor 122 and the new remainder 16,and apply the division lemma to get
122 = 16 x 7 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
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 3624 and 1682 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(122,16) = HCF(260,122) = HCF(1682,260) = HCF(3624,1682) .
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Frequently Asked Questions on HCF of 3624, 1682 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 3624, 1682?
Answer: HCF of 3624, 1682 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3624, 1682 using Euclid's Algorithm?
Answer: For arbitrary numbers 3624, 1682 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.