Highest Common Factor of 842, 658, 316 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 842, 658, 316 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 842, 658, 316 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 842, 658, 316 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 842, 658, 316 is 2.
HCF(842, 658, 316) = 2
HCF of 842, 658, 316 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 842, 658, 316 is 2.
Highest Common Factor of 842,658,316 is 2
Step 1: Since 842 > 658, we apply the division lemma to 842 and 658, to get
842 = 658 x 1 + 184
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 184 and 658, to get
658 = 184 x 3 + 106
Step 3: We consider the new divisor 184 and the new remainder 106, and apply the division lemma to get
184 = 106 x 1 + 78
We consider the new divisor 106 and the new remainder 78,and apply the division lemma to get
106 = 78 x 1 + 28
We consider the new divisor 78 and the new remainder 28,and apply the division lemma to get
78 = 28 x 2 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 842 and 658 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(78,28) = HCF(106,78) = HCF(184,106) = HCF(658,184) = HCF(842,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 316 > 2, we apply the division lemma to 316 and 2, to get
316 = 2 x 158 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 316 is 2
Notice that 2 = HCF(316,2) .
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Frequently Asked Questions on HCF of 842, 658, 316 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 842, 658, 316?
Answer: HCF of 842, 658, 316 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 842, 658, 316 using Euclid's Algorithm?
Answer: For arbitrary numbers 842, 658, 316 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
