Highest Common Factor of 752, 554, 518 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 752, 554, 518 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 554, 518 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 752, 554, 518 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 752, 554, 518 is 2.
HCF(752, 554, 518) = 2
HCF of 752, 554, 518 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 554, 518 is 2.
Highest Common Factor of 752,554,518 is 2
Step 1: Since 752 > 554, we apply the division lemma to 752 and 554, to get
752 = 554 x 1 + 198
Step 2: Since the reminder 554 ≠ 0, we apply division lemma to 198 and 554, to get
554 = 198 x 2 + 158
Step 3: We consider the new divisor 198 and the new remainder 158, and apply the division lemma to get
198 = 158 x 1 + 40
We consider the new divisor 158 and the new remainder 40,and apply the division lemma to get
158 = 40 x 3 + 38
We consider the new divisor 40 and the new remainder 38,and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 752 and 554 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(158,40) = HCF(198,158) = HCF(554,198) = HCF(752,554) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 518 > 2, we apply the division lemma to 518 and 2, to get
518 = 2 x 259 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 518 is 2
Notice that 2 = HCF(518,2) .
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Frequently Asked Questions on HCF of 752, 554, 518 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 752, 554, 518?
Answer: HCF of 752, 554, 518 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 554, 518 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 554, 518 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.