Highest Common Factor of 351, 565 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 351, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 351, 565 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 351, 565 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 351, 565 is 1.
HCF(351, 565) = 1
HCF of 351, 565 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 351, 565 is 1.
Highest Common Factor of 351,565 is 1
Step 1: Since 565 > 351, we apply the division lemma to 565 and 351, to get
565 = 351 x 1 + 214
Step 2: Since the reminder 351 ≠ 0, we apply division lemma to 214 and 351, to get
351 = 214 x 1 + 137
Step 3: We consider the new divisor 214 and the new remainder 137, and apply the division lemma to get
214 = 137 x 1 + 77
We consider the new divisor 137 and the new remainder 77,and apply the division lemma to get
137 = 77 x 1 + 60
We consider the new divisor 77 and the new remainder 60,and apply the division lemma to get
77 = 60 x 1 + 17
We consider the new divisor 60 and the new remainder 17,and apply the division lemma to get
60 = 17 x 3 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 351 and 565 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(60,17) = HCF(77,60) = HCF(137,77) = HCF(214,137) = HCF(351,214) = HCF(565,351) .
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Frequently Asked Questions on HCF of 351, 565 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 351, 565?
Answer: HCF of 351, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 351, 565 using Euclid's Algorithm?
Answer: For arbitrary numbers 351, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.