Highest Common Factor of 3129, 8218 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 3129, 8218 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 3129, 8218 is 7 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 3129, 8218 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 3129, 8218 is 7.
HCF(3129, 8218) = 7
HCF of 3129, 8218 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3129, 8218 is 7.
Highest Common Factor of 3129,8218 is 7
Step 1: Since 8218 > 3129, we apply the division lemma to 8218 and 3129, to get
8218 = 3129 x 2 + 1960
Step 2: Since the reminder 3129 ≠ 0, we apply division lemma to 1960 and 3129, to get
3129 = 1960 x 1 + 1169
Step 3: We consider the new divisor 1960 and the new remainder 1169, and apply the division lemma to get
1960 = 1169 x 1 + 791
We consider the new divisor 1169 and the new remainder 791,and apply the division lemma to get
1169 = 791 x 1 + 378
We consider the new divisor 791 and the new remainder 378,and apply the division lemma to get
791 = 378 x 2 + 35
We consider the new divisor 378 and the new remainder 35,and apply the division lemma to get
378 = 35 x 10 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 3129 and 8218 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(378,35) = HCF(791,378) = HCF(1169,791) = HCF(1960,1169) = HCF(3129,1960) = HCF(8218,3129) .
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Frequently Asked Questions on HCF of 3129, 8218 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 3129, 8218?
Answer: HCF of 3129, 8218 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3129, 8218 using Euclid's Algorithm?
Answer: For arbitrary numbers 3129, 8218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.