Highest Common Factor of 522, 705 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, 705 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 522, 705 is 3 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, 705 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, 705 is 3.
HCF(522, 705) = 3
HCF of 522, 705 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, 705 is 3.
Highest Common Factor of 522,705 is 3
Step 1: Since 705 > 522, we apply the division lemma to 705 and 522, to get
705 = 522 x 1 + 183
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 183 and 522, to get
522 = 183 x 2 + 156
Step 3: We consider the new divisor 183 and the new remainder 156, and apply the division lemma to get
183 = 156 x 1 + 27
We consider the new divisor 156 and the new remainder 27,and apply the division lemma to get
156 = 27 x 5 + 21
We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get
27 = 21 x 1 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 522 and 705 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(156,27) = HCF(183,156) = HCF(522,183) = HCF(705,522) .
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Frequently Asked Questions on HCF of 522, 705 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, 705?
Answer: HCF of 522, 705 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 522, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 522, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.