Highest Common Factor of 3120, 8102 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 3120, 8102 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3120, 8102 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 3120, 8102 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 3120, 8102 is 2.
HCF(3120, 8102) = 2
HCF of 3120, 8102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3120, 8102 is 2.
Highest Common Factor of 3120,8102 is 2
Step 1: Since 8102 > 3120, we apply the division lemma to 8102 and 3120, to get
8102 = 3120 x 2 + 1862
Step 2: Since the reminder 3120 ≠ 0, we apply division lemma to 1862 and 3120, to get
3120 = 1862 x 1 + 1258
Step 3: We consider the new divisor 1862 and the new remainder 1258, and apply the division lemma to get
1862 = 1258 x 1 + 604
We consider the new divisor 1258 and the new remainder 604,and apply the division lemma to get
1258 = 604 x 2 + 50
We consider the new divisor 604 and the new remainder 50,and apply the division lemma to get
604 = 50 x 12 + 4
We consider the new divisor 50 and the new remainder 4,and apply the division lemma to get
50 = 4 x 12 + 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 3120 and 8102 is 2
Notice that 2 = HCF(4,2) = HCF(50,4) = HCF(604,50) = HCF(1258,604) = HCF(1862,1258) = HCF(3120,1862) = HCF(8102,3120) .
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Frequently Asked Questions on HCF of 3120, 8102 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 3120, 8102?
Answer: HCF of 3120, 8102 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3120, 8102 using Euclid's Algorithm?
Answer: For arbitrary numbers 3120, 8102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.