Highest Common Factor of 416, 184, 538, 517 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 416, 184, 538, 517 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 184, 538, 517 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 416, 184, 538, 517 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 416, 184, 538, 517 is 1.
HCF(416, 184, 538, 517) = 1
HCF of 416, 184, 538, 517 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 416, 184, 538, 517 is 1.
Highest Common Factor of 416,184,538,517 is 1
Step 1: Since 416 > 184, we apply the division lemma to 416 and 184, to get
416 = 184 x 2 + 48
Step 2: Since the reminder 184 ≠ 0, we apply division lemma to 48 and 184, to get
184 = 48 x 3 + 40
Step 3: We consider the new divisor 48 and the new remainder 40, and apply the division lemma to get
48 = 40 x 1 + 8
We consider the new divisor 40 and the new remainder 8, and apply the division lemma to get
40 = 8 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 416 and 184 is 8
Notice that 8 = HCF(40,8) = HCF(48,40) = HCF(184,48) = HCF(416,184) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 538 > 8, we apply the division lemma to 538 and 8, to get
538 = 8 x 67 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 538 is 2
Notice that 2 = HCF(8,2) = HCF(538,8) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 517 > 2, we apply the division lemma to 517 and 2, to get
517 = 2 x 258 + 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 517 is 1
Notice that 1 = HCF(2,1) = HCF(517,2) .
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Frequently Asked Questions on HCF of 416, 184, 538, 517 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 416, 184, 538, 517?
Answer: HCF of 416, 184, 538, 517 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 184, 538, 517 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 184, 538, 517 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.