Highest Common Factor of 558, 680 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 558, 680 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 680 is 2 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 558, 680 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 558, 680 is 2.
HCF(558, 680) = 2
HCF of 558, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 680 is 2.
Highest Common Factor of 558,680 is 2
Step 1: Since 680 > 558, we apply the division lemma to 680 and 558, to get
680 = 558 x 1 + 122
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 122 and 558, to get
558 = 122 x 4 + 70
Step 3: We consider the new divisor 122 and the new remainder 70, and apply the division lemma to get
122 = 70 x 1 + 52
We consider the new divisor 70 and the new remainder 52,and apply the division lemma to get
70 = 52 x 1 + 18
We consider the new divisor 52 and the new remainder 18,and apply the division lemma to get
52 = 18 x 2 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 558 and 680 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(52,18) = HCF(70,52) = HCF(122,70) = HCF(558,122) = HCF(680,558) .
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Frequently Asked Questions on HCF of 558, 680 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 558, 680?
Answer: HCF of 558, 680 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.