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 877, 8657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 877, 8657 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 877, 8657 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 877, 8657 is 1.
HCF(877, 8657) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 877, 8657 is 1.
Step 1: Since 8657 > 877, we apply the division lemma to 8657 and 877, to get
8657 = 877 x 9 + 764
Step 2: Since the reminder 877 ≠ 0, we apply division lemma to 764 and 877, to get
877 = 764 x 1 + 113
Step 3: We consider the new divisor 764 and the new remainder 113, and apply the division lemma to get
764 = 113 x 6 + 86
We consider the new divisor 113 and the new remainder 86,and apply the division lemma to get
113 = 86 x 1 + 27
We consider the new divisor 86 and the new remainder 27,and apply the division lemma to get
86 = 27 x 3 + 5
We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get
27 = 5 x 5 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 877 and 8657 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(86,27) = HCF(113,86) = HCF(764,113) = HCF(877,764) = HCF(8657,877) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 877, 8657?
Answer: HCF of 877, 8657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 877, 8657 using Euclid's Algorithm?
Answer: For arbitrary numbers 877, 8657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.