Highest Common Factor of 2210, 4075 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 2210, 4075 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2210, 4075 is 5 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 2210, 4075 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 2210, 4075 is 5.
HCF(2210, 4075) = 5
HCF of 2210, 4075 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2210, 4075 is 5.
Highest Common Factor of 2210,4075 is 5
Step 1: Since 4075 > 2210, we apply the division lemma to 4075 and 2210, to get
4075 = 2210 x 1 + 1865
Step 2: Since the reminder 2210 ≠ 0, we apply division lemma to 1865 and 2210, to get
2210 = 1865 x 1 + 345
Step 3: We consider the new divisor 1865 and the new remainder 345, and apply the division lemma to get
1865 = 345 x 5 + 140
We consider the new divisor 345 and the new remainder 140,and apply the division lemma to get
345 = 140 x 2 + 65
We consider the new divisor 140 and the new remainder 65,and apply the division lemma to get
140 = 65 x 2 + 10
We consider the new divisor 65 and the new remainder 10,and apply the division lemma to get
65 = 10 x 6 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2210 and 4075 is 5
Notice that 5 = HCF(10,5) = HCF(65,10) = HCF(140,65) = HCF(345,140) = HCF(1865,345) = HCF(2210,1865) = HCF(4075,2210) .
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Frequently Asked Questions on HCF of 2210, 4075 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 2210, 4075?
Answer: HCF of 2210, 4075 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2210, 4075 using Euclid's Algorithm?
Answer: For arbitrary numbers 2210, 4075 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.