Highest Common Factor of 512, 668 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 512, 668 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 668 is 4 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 512, 668 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 512, 668 is 4.
HCF(512, 668) = 4
HCF of 512, 668 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 668 is 4.
Highest Common Factor of 512,668 is 4
Step 1: Since 668 > 512, we apply the division lemma to 668 and 512, to get
668 = 512 x 1 + 156
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 156 and 512, to get
512 = 156 x 3 + 44
Step 3: We consider the new divisor 156 and the new remainder 44, and apply the division lemma to get
156 = 44 x 3 + 24
We consider the new divisor 44 and the new remainder 24,and apply the division lemma to get
44 = 24 x 1 + 20
We consider the new divisor 24 and the new remainder 20,and apply the division lemma to get
24 = 20 x 1 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 512 and 668 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(156,44) = HCF(512,156) = HCF(668,512) .
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Frequently Asked Questions on HCF of 512, 668 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 512, 668?
Answer: HCF of 512, 668 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 668 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 668 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.