Highest Common Factor of 987, 680, 613 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 987, 680, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 680, 613 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 987, 680, 613 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 987, 680, 613 is 1.
HCF(987, 680, 613) = 1
HCF of 987, 680, 613 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 987, 680, 613 is 1.
Highest Common Factor of 987,680,613 is 1
Step 1: Since 987 > 680, we apply the division lemma to 987 and 680, to get
987 = 680 x 1 + 307
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 307 and 680, to get
680 = 307 x 2 + 66
Step 3: We consider the new divisor 307 and the new remainder 66, and apply the division lemma to get
307 = 66 x 4 + 43
We consider the new divisor 66 and the new remainder 43,and apply the division lemma to get
66 = 43 x 1 + 23
We consider the new divisor 43 and the new remainder 23,and apply the division lemma to get
43 = 23 x 1 + 20
We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get
23 = 20 x 1 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 987 and 680 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(66,43) = HCF(307,66) = HCF(680,307) = HCF(987,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 613 > 1, we apply the division lemma to 613 and 1, to get
613 = 1 x 613 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 613 is 1
Notice that 1 = HCF(613,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 987, 680, 613 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 987, 680, 613?
Answer: HCF of 987, 680, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 680, 613 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 680, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.