Highest Common Factor of 686, 196, 470 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 686, 196, 470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 686, 196, 470 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 686, 196, 470 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 686, 196, 470 is 2.
HCF(686, 196, 470) = 2
HCF of 686, 196, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 686, 196, 470 is 2.
Highest Common Factor of 686,196,470 is 2
Step 1: Since 686 > 196, we apply the division lemma to 686 and 196, to get
686 = 196 x 3 + 98
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 98 and 196, to get
196 = 98 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 98, the HCF of 686 and 196 is 98
Notice that 98 = HCF(196,98) = HCF(686,196) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 470 > 98, we apply the division lemma to 470 and 98, to get
470 = 98 x 4 + 78
Step 2: Since the reminder 98 ≠ 0, we apply division lemma to 78 and 98, to get
98 = 78 x 1 + 20
Step 3: We consider the new divisor 78 and the new remainder 20, and apply the division lemma to get
78 = 20 x 3 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 98 and 470 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(78,20) = HCF(98,78) = HCF(470,98) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 686, 196, 470 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 686, 196, 470?
Answer: HCF of 686, 196, 470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 686, 196, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 686, 196, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.