Highest Common Factor of 2205, 6170, 67270 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 2205, 6170, 67270 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2205, 6170, 67270 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 2205, 6170, 67270 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 2205, 6170, 67270 is 5.
HCF(2205, 6170, 67270) = 5
HCF of 2205, 6170, 67270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2205, 6170, 67270 is 5.
Highest Common Factor of 2205,6170,67270 is 5
Step 1: Since 6170 > 2205, we apply the division lemma to 6170 and 2205, to get
6170 = 2205 x 2 + 1760
Step 2: Since the reminder 2205 ≠ 0, we apply division lemma to 1760 and 2205, to get
2205 = 1760 x 1 + 445
Step 3: We consider the new divisor 1760 and the new remainder 445, and apply the division lemma to get
1760 = 445 x 3 + 425
We consider the new divisor 445 and the new remainder 425,and apply the division lemma to get
445 = 425 x 1 + 20
We consider the new divisor 425 and the new remainder 20,and apply the division lemma to get
425 = 20 x 21 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2205 and 6170 is 5
Notice that 5 = HCF(20,5) = HCF(425,20) = HCF(445,425) = HCF(1760,445) = HCF(2205,1760) = HCF(6170,2205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 67270 > 5, we apply the division lemma to 67270 and 5, to get
67270 = 5 x 13454 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 67270 is 5
Notice that 5 = HCF(67270,5) .
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Frequently Asked Questions on HCF of 2205, 6170, 67270 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 2205, 6170, 67270?
Answer: HCF of 2205, 6170, 67270 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2205, 6170, 67270 using Euclid's Algorithm?
Answer: For arbitrary numbers 2205, 6170, 67270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.