Highest Common Factor of 754, 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 754, 512 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 512 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 754, 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 754, 512 is 2.
HCF(754, 512) = 2
HCF of 754, 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 754, 512 is 2.
Highest Common Factor of 754,512 is 2
Step 1: Since 754 > 512, we apply the division lemma to 754 and 512, to get
754 = 512 x 1 + 242
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 242 and 512, to get
512 = 242 x 2 + 28
Step 3: We consider the new divisor 242 and the new remainder 28, and apply the division lemma to get
242 = 28 x 8 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 512 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(242,28) = HCF(512,242) = HCF(754,512) .
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Frequently Asked Questions on HCF of 754, 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 754, 512?
Answer: HCF of 754, 512 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 512 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
