Highest Common Factor of 687, 880, 589 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 687, 880, 589 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 687, 880, 589 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 687, 880, 589 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 687, 880, 589 is 1.
HCF(687, 880, 589) = 1
HCF of 687, 880, 589 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 687, 880, 589 is 1.
Highest Common Factor of 687,880,589 is 1
Step 1: Since 880 > 687, we apply the division lemma to 880 and 687, to get
880 = 687 x 1 + 193
Step 2: Since the reminder 687 ≠ 0, we apply division lemma to 193 and 687, to get
687 = 193 x 3 + 108
Step 3: We consider the new divisor 193 and the new remainder 108, and apply the division lemma to get
193 = 108 x 1 + 85
We consider the new divisor 108 and the new remainder 85,and apply the division lemma to get
108 = 85 x 1 + 23
We consider the new divisor 85 and the new remainder 23,and apply the division lemma to get
85 = 23 x 3 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 687 and 880 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(85,23) = HCF(108,85) = HCF(193,108) = HCF(687,193) = HCF(880,687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 589 > 1, we apply the division lemma to 589 and 1, to get
589 = 1 x 589 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 589 is 1
Notice that 1 = HCF(589,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 687, 880, 589 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 687, 880, 589?
Answer: HCF of 687, 880, 589 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 687, 880, 589 using Euclid's Algorithm?
Answer: For arbitrary numbers 687, 880, 589 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.