Highest Common Factor of 522, 199, 916 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 522, 199, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 199, 916 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 522, 199, 916 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 522, 199, 916 is 1.
HCF(522, 199, 916) = 1
HCF of 522, 199, 916 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 522, 199, 916 is 1.
Highest Common Factor of 522,199,916 is 1
Step 1: Since 522 > 199, we apply the division lemma to 522 and 199, to get
522 = 199 x 2 + 124
Step 2: Since the reminder 199 ≠ 0, we apply division lemma to 124 and 199, to get
199 = 124 x 1 + 75
Step 3: We consider the new divisor 124 and the new remainder 75, and apply the division lemma to get
124 = 75 x 1 + 49
We consider the new divisor 75 and the new remainder 49,and apply the division lemma to get
75 = 49 x 1 + 26
We consider the new divisor 49 and the new remainder 26,and apply the division lemma to get
49 = 26 x 1 + 23
We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get
26 = 23 x 1 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 522 and 199 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(49,26) = HCF(75,49) = HCF(124,75) = HCF(199,124) = HCF(522,199) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 1, we apply the division lemma to 916 and 1, to get
916 = 1 x 916 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 916 is 1
Notice that 1 = HCF(916,1) .
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Frequently Asked Questions on HCF of 522, 199, 916 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 522, 199, 916?
Answer: HCF of 522, 199, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 199, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 199, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.