Highest Common Factor of 882, 6854 using Euclid's algorithm
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 882, 6854 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 882, 6854 is 2 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 882, 6854 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 882, 6854 is 2.
HCF(882, 6854) = 2
HCF of 882, 6854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 882, 6854 is 2.
Highest Common Factor of 882,6854 is 2
Step 1: Since 6854 > 882, we apply the division lemma to 6854 and 882, to get
6854 = 882 x 7 + 680
Step 2: Since the reminder 882 ≠ 0, we apply division lemma to 680 and 882, to get
882 = 680 x 1 + 202
Step 3: We consider the new divisor 680 and the new remainder 202, and apply the division lemma to get
680 = 202 x 3 + 74
We consider the new divisor 202 and the new remainder 74,and apply the division lemma to get
202 = 74 x 2 + 54
We consider the new divisor 74 and the new remainder 54,and apply the division lemma to get
74 = 54 x 1 + 20
We consider the new divisor 54 and the new remainder 20,and apply the division lemma to get
54 = 20 x 2 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 882 and 6854 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(54,20) = HCF(74,54) = HCF(202,74) = HCF(680,202) = HCF(882,680) = HCF(6854,882) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 882, 6854 using Euclid's Algorithm
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 882, 6854?
Answer: HCF of 882, 6854 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 882, 6854 using Euclid's Algorithm?
Answer: For arbitrary numbers 882, 6854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.