Highest Common Factor of 416, 654, 522 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, 654, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 416, 654, 522 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 416, 654, 522 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, 654, 522 is 2.
HCF(416, 654, 522) = 2
HCF of 416, 654, 522 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, 654, 522 is 2.
Highest Common Factor of 416,654,522 is 2
Step 1: Since 654 > 416, we apply the division lemma to 654 and 416, to get
654 = 416 x 1 + 238
Step 2: Since the reminder 416 ≠ 0, we apply division lemma to 238 and 416, to get
416 = 238 x 1 + 178
Step 3: We consider the new divisor 238 and the new remainder 178, and apply the division lemma to get
238 = 178 x 1 + 60
We consider the new divisor 178 and the new remainder 60,and apply the division lemma to get
178 = 60 x 2 + 58
We consider the new divisor 60 and the new remainder 58,and apply the division lemma to get
60 = 58 x 1 + 2
We consider the new divisor 58 and the new remainder 2,and apply the division lemma to get
58 = 2 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 416 and 654 is 2
Notice that 2 = HCF(58,2) = HCF(60,58) = HCF(178,60) = HCF(238,178) = HCF(416,238) = HCF(654,416) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 522 > 2, we apply the division lemma to 522 and 2, to get
522 = 2 x 261 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 522 is 2
Notice that 2 = HCF(522,2) .
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Frequently Asked Questions on HCF of 416, 654, 522 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, 654, 522?
Answer: HCF of 416, 654, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 416, 654, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 416, 654, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.