Highest Common Factor of 684, 874, 882 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 684, 874, 882 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 874, 882 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 684, 874, 882 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 684, 874, 882 is 2.
HCF(684, 874, 882) = 2
HCF of 684, 874, 882 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 874, 882 is 2.
Highest Common Factor of 684,874,882 is 2
Step 1: Since 874 > 684, we apply the division lemma to 874 and 684, to get
874 = 684 x 1 + 190
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 190 and 684, to get
684 = 190 x 3 + 114
Step 3: We consider the new divisor 190 and the new remainder 114, and apply the division lemma to get
190 = 114 x 1 + 76
We consider the new divisor 114 and the new remainder 76,and apply the division lemma to get
114 = 76 x 1 + 38
We consider the new divisor 76 and the new remainder 38,and apply the division lemma to get
76 = 38 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 38, the HCF of 684 and 874 is 38
Notice that 38 = HCF(76,38) = HCF(114,76) = HCF(190,114) = HCF(684,190) = HCF(874,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 882 > 38, we apply the division lemma to 882 and 38, to get
882 = 38 x 23 + 8
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 8 and 38, to get
38 = 8 x 4 + 6
Step 3: We consider the new divisor 8 and the new remainder 6, and apply the division lemma to get
8 = 6 x 1 + 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 38 and 882 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(38,8) = HCF(882,38) .
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Frequently Asked Questions on HCF of 684, 874, 882 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 684, 874, 882?
Answer: HCF of 684, 874, 882 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 874, 882 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 874, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.