Highest Common Factor of 869, 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 869, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 869, 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 869, 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 869, 680 is 1.
HCF(869, 680) = 1
HCF of 869, 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 869, 680 is 1.
Highest Common Factor of 869,680 is 1
Step 1: Since 869 > 680, we apply the division lemma to 869 and 680, to get
869 = 680 x 1 + 189
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 189 and 680, to get
680 = 189 x 3 + 113
Step 3: We consider the new divisor 189 and the new remainder 113, and apply the division lemma to get
189 = 113 x 1 + 76
We consider the new divisor 113 and the new remainder 76,and apply the division lemma to get
113 = 76 x 1 + 37
We consider the new divisor 76 and the new remainder 37,and apply the division lemma to get
76 = 37 x 2 + 2
We consider the new divisor 37 and the new remainder 2,and apply the division lemma to get
37 = 2 x 18 + 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 869 and 680 is 1
Notice that 1 = HCF(2,1) = HCF(37,2) = HCF(76,37) = HCF(113,76) = HCF(189,113) = HCF(680,189) = HCF(869,680) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 869, 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 869, 680?
Answer: HCF of 869, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 869, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 869, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.