Highest Common Factor of 987, 8731, 9677 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, 8731, 9677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 987, 8731, 9677 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, 8731, 9677 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, 8731, 9677 is 1.
HCF(987, 8731, 9677) = 1
HCF of 987, 8731, 9677 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, 8731, 9677 is 1.
Highest Common Factor of 987,8731,9677 is 1
Step 1: Since 8731 > 987, we apply the division lemma to 8731 and 987, to get
8731 = 987 x 8 + 835
Step 2: Since the reminder 987 ≠ 0, we apply division lemma to 835 and 987, to get
987 = 835 x 1 + 152
Step 3: We consider the new divisor 835 and the new remainder 152, and apply the division lemma to get
835 = 152 x 5 + 75
We consider the new divisor 152 and the new remainder 75,and apply the division lemma to get
152 = 75 x 2 + 2
We consider the new divisor 75 and the new remainder 2,and apply the division lemma to get
75 = 2 x 37 + 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 8731 is 1
Notice that 1 = HCF(2,1) = HCF(75,2) = HCF(152,75) = HCF(835,152) = HCF(987,835) = HCF(8731,987) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9677 > 1, we apply the division lemma to 9677 and 1, to get
9677 = 1 x 9677 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9677 is 1
Notice that 1 = HCF(9677,1) .
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, 8731, 9677 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, 8731, 9677?
Answer: HCF of 987, 8731, 9677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 987, 8731, 9677 using Euclid's Algorithm?
Answer: For arbitrary numbers 987, 8731, 9677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.