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 191, 877, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 191, 877, 205 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 191, 877, 205 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 191, 877, 205 is 1.
HCF(191, 877, 205) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 191, 877, 205 is 1.
Step 1: Since 877 > 191, we apply the division lemma to 877 and 191, to get
877 = 191 x 4 + 113
Step 2: Since the reminder 191 ≠ 0, we apply division lemma to 113 and 191, to get
191 = 113 x 1 + 78
Step 3: We consider the new divisor 113 and the new remainder 78, and apply the division lemma to get
113 = 78 x 1 + 35
We consider the new divisor 78 and the new remainder 35,and apply the division lemma to get
78 = 35 x 2 + 8
We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get
35 = 8 x 4 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 191 and 877 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(78,35) = HCF(113,78) = HCF(191,113) = HCF(877,191) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 205 > 1, we apply the division lemma to 205 and 1, to get
205 = 1 x 205 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 205 is 1
Notice that 1 = HCF(205,1) .
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 191, 877, 205?
Answer: HCF of 191, 877, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 191, 877, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 191, 877, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.