Highest Common Factor of 987, 5791, 6749 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, 5791, 6749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 5791, 6749 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, 5791, 6749 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, 5791, 6749 is 1.
HCF(987, 5791, 6749) = 1
HCF of 987, 5791, 6749 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, 5791, 6749 is 1.
Highest Common Factor of 987,5791,6749 is 1
Step 1: Since 5791 > 987, we apply the division lemma to 5791 and 987, to get
5791 = 987 x 5 + 856
Step 2: Since the reminder 987 ≠ 0, we apply division lemma to 856 and 987, to get
987 = 856 x 1 + 131
Step 3: We consider the new divisor 856 and the new remainder 131, and apply the division lemma to get
856 = 131 x 6 + 70
We consider the new divisor 131 and the new remainder 70,and apply the division lemma to get
131 = 70 x 1 + 61
We consider the new divisor 70 and the new remainder 61,and apply the division lemma to get
70 = 61 x 1 + 9
We consider the new divisor 61 and the new remainder 9,and apply the division lemma to get
61 = 9 x 6 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 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 987 and 5791 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(61,9) = HCF(70,61) = HCF(131,70) = HCF(856,131) = HCF(987,856) = HCF(5791,987) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6749 > 1, we apply the division lemma to 6749 and 1, to get
6749 = 1 x 6749 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6749 is 1
Notice that 1 = HCF(6749,1) .
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, 5791, 6749 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, 5791, 6749?
Answer: HCF of 987, 5791, 6749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 5791, 6749 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 5791, 6749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
