Highest Common Factor of 204, 1677, 3612 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 204, 1677, 3612 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 1677, 3612 is 3 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 204, 1677, 3612 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 204, 1677, 3612 is 3.
HCF(204, 1677, 3612) = 3
HCF of 204, 1677, 3612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 204, 1677, 3612 is 3.
Highest Common Factor of 204,1677,3612 is 3
Step 1: Since 1677 > 204, we apply the division lemma to 1677 and 204, to get
1677 = 204 x 8 + 45
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 45 and 204, to get
204 = 45 x 4 + 24
Step 3: We consider the new divisor 45 and the new remainder 24, and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 204 and 1677 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(204,45) = HCF(1677,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3612 > 3, we apply the division lemma to 3612 and 3, to get
3612 = 3 x 1204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 3612 is 3
Notice that 3 = HCF(3612,3) .
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Frequently Asked Questions on HCF of 204, 1677, 3612 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 204, 1677, 3612?
Answer: HCF of 204, 1677, 3612 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 1677, 3612 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 1677, 3612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.