Highest Common Factor of 368, 6820, 6654 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 368, 6820, 6654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 368, 6820, 6654 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 368, 6820, 6654 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 368, 6820, 6654 is 2.
HCF(368, 6820, 6654) = 2
HCF of 368, 6820, 6654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 368, 6820, 6654 is 2.
Highest Common Factor of 368,6820,6654 is 2
Step 1: Since 6820 > 368, we apply the division lemma to 6820 and 368, to get
6820 = 368 x 18 + 196
Step 2: Since the reminder 368 ≠ 0, we apply division lemma to 196 and 368, to get
368 = 196 x 1 + 172
Step 3: We consider the new divisor 196 and the new remainder 172, and apply the division lemma to get
196 = 172 x 1 + 24
We consider the new divisor 172 and the new remainder 24,and apply the division lemma to get
172 = 24 x 7 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 368 and 6820 is 4
Notice that 4 = HCF(24,4) = HCF(172,24) = HCF(196,172) = HCF(368,196) = HCF(6820,368) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6654 > 4, we apply the division lemma to 6654 and 4, to get
6654 = 4 x 1663 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 6654 is 2
Notice that 2 = HCF(4,2) = HCF(6654,4) .
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Frequently Asked Questions on HCF of 368, 6820, 6654 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 368, 6820, 6654?
Answer: HCF of 368, 6820, 6654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 368, 6820, 6654 using Euclid's Algorithm?
Answer: For arbitrary numbers 368, 6820, 6654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.