Highest Common Factor of 559, 678 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 559, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 559, 678 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 559, 678 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 559, 678 is 1.
HCF(559, 678) = 1
HCF of 559, 678 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 559, 678 is 1.
Highest Common Factor of 559,678 is 1
Step 1: Since 678 > 559, we apply the division lemma to 678 and 559, to get
678 = 559 x 1 + 119
Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 119 and 559, to get
559 = 119 x 4 + 83
Step 3: We consider the new divisor 119 and the new remainder 83, and apply the division lemma to get
119 = 83 x 1 + 36
We consider the new divisor 83 and the new remainder 36,and apply the division lemma to get
83 = 36 x 2 + 11
We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get
36 = 11 x 3 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 559 and 678 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(83,36) = HCF(119,83) = HCF(559,119) = HCF(678,559) .
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Frequently Asked Questions on HCF of 559, 678 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 559, 678?
Answer: HCF of 559, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 559, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 559, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.