Highest Common Factor of 529, 759, 51 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 529, 759, 51 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 529, 759, 51 is 1 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 529, 759, 51 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 529, 759, 51 is 1.
HCF(529, 759, 51) = 1
HCF of 529, 759, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 529, 759, 51 is 1.
Highest Common Factor of 529,759,51 is 1
Step 1: Since 759 > 529, we apply the division lemma to 759 and 529, to get
759 = 529 x 1 + 230
Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 230 and 529, to get
529 = 230 x 2 + 69
Step 3: We consider the new divisor 230 and the new remainder 69, and apply the division lemma to get
230 = 69 x 3 + 23
We consider the new divisor 69 and the new remainder 23, and apply the division lemma to get
69 = 23 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 529 and 759 is 23
Notice that 23 = HCF(69,23) = HCF(230,69) = HCF(529,230) = HCF(759,529) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 23, we apply the division lemma to 51 and 23, to get
51 = 23 x 2 + 5
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 5 and 23, to get
23 = 5 x 4 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 23 and 51 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(51,23) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 529, 759, 51 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 529, 759, 51?
Answer: HCF of 529, 759, 51 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 529, 759, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 529, 759, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.