Highest Common Factor of 565, 666 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, 666 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 565, 666 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, 666 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, 666 is 1.
HCF(565, 666) = 1
HCF of 565, 666 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, 666 is 1.
Highest Common Factor of 565,666 is 1
Step 1: Since 666 > 565, we apply the division lemma to 666 and 565, to get
666 = 565 x 1 + 101
Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 101 and 565, to get
565 = 101 x 5 + 60
Step 3: We consider the new divisor 101 and the new remainder 60, and apply the division lemma to get
101 = 60 x 1 + 41
We consider the new divisor 60 and the new remainder 41,and apply the division lemma to get
60 = 41 x 1 + 19
We consider the new divisor 41 and the new remainder 19,and apply the division lemma to get
41 = 19 x 2 + 3
We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get
19 = 3 x 6 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 666 is 1
Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(41,19) = HCF(60,41) = HCF(101,60) = HCF(565,101) = HCF(666,565) .
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Frequently Asked Questions on HCF of 565, 666 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, 666?
Answer: HCF of 565, 666 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 565, 666 using Euclid's Algorithm?
Answer: For arbitrary numbers 565, 666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.