Highest Common Factor of 608, 65559 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 608, 65559 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 65559 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 608, 65559 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 608, 65559 is 1.
HCF(608, 65559) = 1
HCF of 608, 65559 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 65559 is 1.
Highest Common Factor of 608,65559 is 1
Step 1: Since 65559 > 608, we apply the division lemma to 65559 and 608, to get
65559 = 608 x 107 + 503
Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 503 and 608, to get
608 = 503 x 1 + 105
Step 3: We consider the new divisor 503 and the new remainder 105, and apply the division lemma to get
503 = 105 x 4 + 83
We consider the new divisor 105 and the new remainder 83,and apply the division lemma to get
105 = 83 x 1 + 22
We consider the new divisor 83 and the new remainder 22,and apply the division lemma to get
83 = 22 x 3 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 608 and 65559 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(83,22) = HCF(105,83) = HCF(503,105) = HCF(608,503) = HCF(65559,608) .
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Frequently Asked Questions on HCF of 608, 65559 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 608, 65559?
Answer: HCF of 608, 65559 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 65559 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 65559 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.