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 868, 6781, 2946 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 868, 6781, 2946 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 868, 6781, 2946 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 868, 6781, 2946 is 1.
HCF(868, 6781, 2946) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 868, 6781, 2946 is 1.
Step 1: Since 6781 > 868, we apply the division lemma to 6781 and 868, to get
6781 = 868 x 7 + 705
Step 2: Since the reminder 868 ≠ 0, we apply division lemma to 705 and 868, to get
868 = 705 x 1 + 163
Step 3: We consider the new divisor 705 and the new remainder 163, and apply the division lemma to get
705 = 163 x 4 + 53
We consider the new divisor 163 and the new remainder 53,and apply the division lemma to get
163 = 53 x 3 + 4
We consider the new divisor 53 and the new remainder 4,and apply the division lemma to get
53 = 4 x 13 + 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 868 and 6781 is 1
Notice that 1 = HCF(4,1) = HCF(53,4) = HCF(163,53) = HCF(705,163) = HCF(868,705) = HCF(6781,868) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2946 > 1, we apply the division lemma to 2946 and 1, to get
2946 = 1 x 2946 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2946 is 1
Notice that 1 = HCF(2946,1) .
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 868, 6781, 2946?
Answer: HCF of 868, 6781, 2946 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 868, 6781, 2946 using Euclid's Algorithm?
Answer: For arbitrary numbers 868, 6781, 2946 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.