Highest Common Factor of 204, 722, 417 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, 722, 417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 722, 417 is 1 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, 722, 417 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, 722, 417 is 1.
HCF(204, 722, 417) = 1
HCF of 204, 722, 417 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, 722, 417 is 1.
Highest Common Factor of 204,722,417 is 1
Step 1: Since 722 > 204, we apply the division lemma to 722 and 204, to get
722 = 204 x 3 + 110
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 110 and 204, to get
204 = 110 x 1 + 94
Step 3: We consider the new divisor 110 and the new remainder 94, and apply the division lemma to get
110 = 94 x 1 + 16
We consider the new divisor 94 and the new remainder 16,and apply the division lemma to get
94 = 16 x 5 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 204 and 722 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(94,16) = HCF(110,94) = HCF(204,110) = HCF(722,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 417 > 2, we apply the division lemma to 417 and 2, to get
417 = 2 x 208 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 417 is 1
Notice that 1 = HCF(2,1) = HCF(417,2) .
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Frequently Asked Questions on HCF of 204, 722, 417 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, 722, 417?
Answer: HCF of 204, 722, 417 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 722, 417 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 722, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
