Highest Common Factor of 620, 217, 680 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 620, 217, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 620, 217, 680 is 1 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 620, 217, 680 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 620, 217, 680 is 1.
HCF(620, 217, 680) = 1
HCF of 620, 217, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 620, 217, 680 is 1.
Highest Common Factor of 620,217,680 is 1
Step 1: Since 620 > 217, we apply the division lemma to 620 and 217, to get
620 = 217 x 2 + 186
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 186 and 217, to get
217 = 186 x 1 + 31
Step 3: We consider the new divisor 186 and the new remainder 31, and apply the division lemma to get
186 = 31 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 31, the HCF of 620 and 217 is 31
Notice that 31 = HCF(186,31) = HCF(217,186) = HCF(620,217) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 31, we apply the division lemma to 680 and 31, to get
680 = 31 x 21 + 29
Step 2: Since the reminder 31 ≠ 0, we apply division lemma to 29 and 31, to get
31 = 29 x 1 + 2
Step 3: We consider the new divisor 29 and the new remainder 2, and apply the division lemma to get
29 = 2 x 14 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 31 and 680 is 1
Notice that 1 = HCF(2,1) = HCF(29,2) = HCF(31,29) = HCF(680,31) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 620, 217, 680 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 620, 217, 680?
Answer: HCF of 620, 217, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 620, 217, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 620, 217, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.