Highest Common Factor of 364, 862, 54 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 364, 862, 54 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 364, 862, 54 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 364, 862, 54 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 364, 862, 54 is 2.
HCF(364, 862, 54) = 2
HCF of 364, 862, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 364, 862, 54 is 2.
Highest Common Factor of 364,862,54 is 2
Step 1: Since 862 > 364, we apply the division lemma to 862 and 364, to get
862 = 364 x 2 + 134
Step 2: Since the reminder 364 ≠ 0, we apply division lemma to 134 and 364, to get
364 = 134 x 2 + 96
Step 3: We consider the new divisor 134 and the new remainder 96, and apply the division lemma to get
134 = 96 x 1 + 38
We consider the new divisor 96 and the new remainder 38,and apply the division lemma to get
96 = 38 x 2 + 20
We consider the new divisor 38 and the new remainder 20,and apply the division lemma to get
38 = 20 x 1 + 18
We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get
20 = 18 x 1 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 364 and 862 is 2
Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(38,20) = HCF(96,38) = HCF(134,96) = HCF(364,134) = HCF(862,364) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 2, we apply the division lemma to 54 and 2, to get
54 = 2 x 27 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 54 is 2
Notice that 2 = HCF(54,2) .
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Frequently Asked Questions on HCF of 364, 862, 54 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 364, 862, 54?
Answer: HCF of 364, 862, 54 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 364, 862, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 364, 862, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.