Highest Common Factor of 868, 512 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 868, 512 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 868, 512 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 868, 512 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 868, 512 is 4.
HCF(868, 512) = 4
HCF of 868, 512 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 868, 512 is 4.
Highest Common Factor of 868,512 is 4
Step 1: Since 868 > 512, we apply the division lemma to 868 and 512, to get
868 = 512 x 1 + 356
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 356 and 512, to get
512 = 356 x 1 + 156
Step 3: We consider the new divisor 356 and the new remainder 156, and apply the division lemma to get
356 = 156 x 2 + 44
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 868 and 512 is 4
Notice that 4 = HCF(20,4) = HCF(24,20) = HCF(44,24) = HCF(156,44) = HCF(356,156) = HCF(512,356) = HCF(868,512) .
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Frequently Asked Questions on HCF of 868, 512 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 868, 512?
Answer: HCF of 868, 512 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 868, 512 using Euclid's Algorithm?
Answer: For arbitrary numbers 868, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.