Highest Common Factor of 107, 658 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 107, 658 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 107, 658 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 107, 658 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 107, 658 is 1.
HCF(107, 658) = 1
HCF of 107, 658 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 107, 658 is 1.
Highest Common Factor of 107,658 is 1
Step 1: Since 658 > 107, we apply the division lemma to 658 and 107, to get
658 = 107 x 6 + 16
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 16 and 107, to get
107 = 16 x 6 + 11
Step 3: We consider the new divisor 16 and the new remainder 11, and apply the division lemma to get
16 = 11 x 1 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 107 and 658 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(107,16) = HCF(658,107) .
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Frequently Asked Questions on HCF of 107, 658 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 107, 658?
Answer: HCF of 107, 658 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 107, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 107, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.