Highest Common Factor of 659, 205, 566, 10 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 659, 205, 566, 10 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 659, 205, 566, 10 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 659, 205, 566, 10 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 659, 205, 566, 10 is 1.
HCF(659, 205, 566, 10) = 1
HCF of 659, 205, 566, 10 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 659, 205, 566, 10 is 1.
Highest Common Factor of 659,205,566,10 is 1
Step 1: Since 659 > 205, we apply the division lemma to 659 and 205, to get
659 = 205 x 3 + 44
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 44 and 205, to get
205 = 44 x 4 + 29
Step 3: We consider the new divisor 44 and the new remainder 29, and apply the division lemma to get
44 = 29 x 1 + 15
We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get
29 = 15 x 1 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 659 and 205 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(44,29) = HCF(205,44) = HCF(659,205) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 566 > 1, we apply the division lemma to 566 and 1, to get
566 = 1 x 566 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 566 is 1
Notice that 1 = HCF(566,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
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Frequently Asked Questions on HCF of 659, 205, 566, 10 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 659, 205, 566, 10?
Answer: HCF of 659, 205, 566, 10 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 659, 205, 566, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 659, 205, 566, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
