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 311, 9476, 8969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 311, 9476, 8969 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 311, 9476, 8969 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 311, 9476, 8969 is 1.
HCF(311, 9476, 8969) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 311, 9476, 8969 is 1.
Step 1: Since 9476 > 311, we apply the division lemma to 9476 and 311, to get
9476 = 311 x 30 + 146
Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 146 and 311, to get
311 = 146 x 2 + 19
Step 3: We consider the new divisor 146 and the new remainder 19, and apply the division lemma to get
146 = 19 x 7 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 311 and 9476 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(146,19) = HCF(311,146) = HCF(9476,311) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8969 > 1, we apply the division lemma to 8969 and 1, to get
8969 = 1 x 8969 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8969 is 1
Notice that 1 = HCF(8969,1) .
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 311, 9476, 8969?
Answer: HCF of 311, 9476, 8969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 311, 9476, 8969 using Euclid's Algorithm?
Answer: For arbitrary numbers 311, 9476, 8969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.