Highest Common Factor of 868, 174, 689 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 868, 174, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 868, 174, 689 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 868, 174, 689 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 868, 174, 689 is 1.
HCF(868, 174, 689) = 1
HCF of 868, 174, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 868, 174, 689 is 1.
Highest Common Factor of 868,174,689 is 1
Step 1: Since 868 > 174, we apply the division lemma to 868 and 174, to get
868 = 174 x 4 + 172
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 172 and 174, to get
174 = 172 x 1 + 2
Step 3: We consider the new divisor 172 and the new remainder 2, and apply the division lemma to get
172 = 2 x 86 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 868 and 174 is 2
Notice that 2 = HCF(172,2) = HCF(174,172) = HCF(868,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 689 > 2, we apply the division lemma to 689 and 2, to get
689 = 2 x 344 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 689 is 1
Notice that 1 = HCF(2,1) = HCF(689,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 868, 174, 689 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 868, 174, 689?
Answer: HCF of 868, 174, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 868, 174, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 868, 174, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.