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 2971, 6677 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2971, 6677 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 2971, 6677 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 2971, 6677 is 1.
HCF(2971, 6677) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2971, 6677 is 1.
Step 1: Since 6677 > 2971, we apply the division lemma to 6677 and 2971, to get
6677 = 2971 x 2 + 735
Step 2: Since the reminder 2971 ≠ 0, we apply division lemma to 735 and 2971, to get
2971 = 735 x 4 + 31
Step 3: We consider the new divisor 735 and the new remainder 31, and apply the division lemma to get
735 = 31 x 23 + 22
We consider the new divisor 31 and the new remainder 22,and apply the division lemma to get
31 = 22 x 1 + 9
We consider the new divisor 22 and the new remainder 9,and apply the division lemma to get
22 = 9 x 2 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2971 and 6677 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(22,9) = HCF(31,22) = HCF(735,31) = HCF(2971,735) = HCF(6677,2971) .
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 2971, 6677?
Answer: HCF of 2971, 6677 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2971, 6677 using Euclid's Algorithm?
Answer: For arbitrary numbers 2971, 6677 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.