Highest Common Factor of 6120, 2270 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 6120, 2270 i.e. 10 the largest integer that leaves a remainder zero for all numbers.
HCF of 6120, 2270 is 10 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 6120, 2270 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 6120, 2270 is 10.
HCF(6120, 2270) = 10
HCF of 6120, 2270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6120, 2270 is 10.
Highest Common Factor of 6120,2270 is 10
Step 1: Since 6120 > 2270, we apply the division lemma to 6120 and 2270, to get
6120 = 2270 x 2 + 1580
Step 2: Since the reminder 2270 ≠ 0, we apply division lemma to 1580 and 2270, to get
2270 = 1580 x 1 + 690
Step 3: We consider the new divisor 1580 and the new remainder 690, and apply the division lemma to get
1580 = 690 x 2 + 200
We consider the new divisor 690 and the new remainder 200,and apply the division lemma to get
690 = 200 x 3 + 90
We consider the new divisor 200 and the new remainder 90,and apply the division lemma to get
200 = 90 x 2 + 20
We consider the new divisor 90 and the new remainder 20,and apply the division lemma to get
90 = 20 x 4 + 10
We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 6120 and 2270 is 10
Notice that 10 = HCF(20,10) = HCF(90,20) = HCF(200,90) = HCF(690,200) = HCF(1580,690) = HCF(2270,1580) = HCF(6120,2270) .
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Frequently Asked Questions on HCF of 6120, 2270 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 6120, 2270?
Answer: HCF of 6120, 2270 is 10 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6120, 2270 using Euclid's Algorithm?
Answer: For arbitrary numbers 6120, 2270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.