Highest Common Factor of 768, 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 768, 658 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 768, 658 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 768, 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 768, 658 is 2.
HCF(768, 658) = 2
HCF of 768, 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 768, 658 is 2.
Highest Common Factor of 768,658 is 2
Step 1: Since 768 > 658, we apply the division lemma to 768 and 658, to get
768 = 658 x 1 + 110
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 110 and 658, to get
658 = 110 x 5 + 108
Step 3: We consider the new divisor 110 and the new remainder 108, and apply the division lemma to get
110 = 108 x 1 + 2
We consider the new divisor 108 and the new remainder 2, and apply the division lemma to get
108 = 2 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 768 and 658 is 2
Notice that 2 = HCF(108,2) = HCF(110,108) = HCF(658,110) = HCF(768,658) .
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Frequently Asked Questions on HCF of 768, 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 768, 658?
Answer: HCF of 768, 658 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 768, 658 using Euclid's Algorithm?
Answer: For arbitrary numbers 768, 658 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
