Highest Common Factor of 558, 965, 657 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, 965, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 965, 657 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 558, 965, 657 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, 965, 657 is 1.
HCF(558, 965, 657) = 1
HCF of 558, 965, 657 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, 965, 657 is 1.
Highest Common Factor of 558,965,657 is 1
Step 1: Since 965 > 558, we apply the division lemma to 965 and 558, to get
965 = 558 x 1 + 407
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 407 and 558, to get
558 = 407 x 1 + 151
Step 3: We consider the new divisor 407 and the new remainder 151, and apply the division lemma to get
407 = 151 x 2 + 105
We consider the new divisor 151 and the new remainder 105,and apply the division lemma to get
151 = 105 x 1 + 46
We consider the new divisor 105 and the new remainder 46,and apply the division lemma to get
105 = 46 x 2 + 13
We consider the new divisor 46 and the new remainder 13,and apply the division lemma to get
46 = 13 x 3 + 7
We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 558 and 965 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(46,13) = HCF(105,46) = HCF(151,105) = HCF(407,151) = HCF(558,407) = HCF(965,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 657 > 1, we apply the division lemma to 657 and 1, to get
657 = 1 x 657 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 657 is 1
Notice that 1 = HCF(657,1) .
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Frequently Asked Questions on HCF of 558, 965, 657 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, 965, 657?
Answer: HCF of 558, 965, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 965, 657 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 965, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.