Highest Common Factor of 522, 362, 46 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, 362, 46 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 362, 46 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 522, 362, 46 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, 362, 46 is 2.
HCF(522, 362, 46) = 2
HCF of 522, 362, 46 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, 362, 46 is 2.
Highest Common Factor of 522,362,46 is 2
Step 1: Since 522 > 362, we apply the division lemma to 522 and 362, to get
522 = 362 x 1 + 160
Step 2: Since the reminder 362 ≠ 0, we apply division lemma to 160 and 362, to get
362 = 160 x 2 + 42
Step 3: We consider the new divisor 160 and the new remainder 42, and apply the division lemma to get
160 = 42 x 3 + 34
We consider the new divisor 42 and the new remainder 34,and apply the division lemma to get
42 = 34 x 1 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma 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 522 and 362 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(42,34) = HCF(160,42) = HCF(362,160) = HCF(522,362) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 46 > 2, we apply the division lemma to 46 and 2, to get
46 = 2 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 46 is 2
Notice that 2 = HCF(46,2) .
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Frequently Asked Questions on HCF of 522, 362, 46 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, 362, 46?
Answer: HCF of 522, 362, 46 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 362, 46 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 362, 46 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.