Highest Common Factor of 382, 658, 840 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 382, 658, 840 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 382, 658, 840 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 382, 658, 840 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 382, 658, 840 is 2.
HCF(382, 658, 840) = 2
HCF of 382, 658, 840 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 382, 658, 840 is 2.
Highest Common Factor of 382,658,840 is 2
Step 1: Since 658 > 382, we apply the division lemma to 658 and 382, to get
658 = 382 x 1 + 276
Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 276 and 382, to get
382 = 276 x 1 + 106
Step 3: We consider the new divisor 276 and the new remainder 106, and apply the division lemma to get
276 = 106 x 2 + 64
We consider the new divisor 106 and the new remainder 64,and apply the division lemma to get
106 = 64 x 1 + 42
We consider the new divisor 64 and the new remainder 42,and apply the division lemma to get
64 = 42 x 1 + 22
We consider the new divisor 42 and the new remainder 22,and apply the division lemma to get
42 = 22 x 1 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 382 and 658 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(42,22) = HCF(64,42) = HCF(106,64) = HCF(276,106) = HCF(382,276) = HCF(658,382) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 840 > 2, we apply the division lemma to 840 and 2, to get
840 = 2 x 420 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 840 is 2
Notice that 2 = HCF(840,2) .
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Frequently Asked Questions on HCF of 382, 658, 840 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 382, 658, 840?
Answer: HCF of 382, 658, 840 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 382, 658, 840 using Euclid's Algorithm?
Answer: For arbitrary numbers 382, 658, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.