Highest Common Factor of 565, 909, 65 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 565, 909, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 909, 65 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 565, 909, 65 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 565, 909, 65 is 1.
HCF(565, 909, 65) = 1
HCF of 565, 909, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 565, 909, 65 is 1.
Highest Common Factor of 565,909,65 is 1
Step 1: Since 909 > 565, we apply the division lemma to 909 and 565, to get
909 = 565 x 1 + 344
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 344 and 565, to get
565 = 344 x 1 + 221
Step 3: We consider the new divisor 344 and the new remainder 221, and apply the division lemma to get
344 = 221 x 1 + 123
We consider the new divisor 221 and the new remainder 123,and apply the division lemma to get
221 = 123 x 1 + 98
We consider the new divisor 123 and the new remainder 98,and apply the division lemma to get
123 = 98 x 1 + 25
We consider the new divisor 98 and the new remainder 25,and apply the division lemma to get
98 = 25 x 3 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 565 and 909 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(98,25) = HCF(123,98) = HCF(221,123) = HCF(344,221) = HCF(565,344) = HCF(909,565) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 1, we apply the division lemma to 65 and 1, to get
65 = 1 x 65 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 65 is 1
Notice that 1 = HCF(65,1) .
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Frequently Asked Questions on HCF of 565, 909, 65 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 565, 909, 65?
Answer: HCF of 565, 909, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 909, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 909, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.