Highest Common Factor of 735, 854, 529 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 735, 854, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 854, 529 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 735, 854, 529 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 735, 854, 529 is 1.
HCF(735, 854, 529) = 1
HCF of 735, 854, 529 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 735, 854, 529 is 1.
Highest Common Factor of 735,854,529 is 1
Step 1: Since 854 > 735, we apply the division lemma to 854 and 735, to get
854 = 735 x 1 + 119
Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 119 and 735, to get
735 = 119 x 6 + 21
Step 3: We consider the new divisor 119 and the new remainder 21, and apply the division lemma to get
119 = 21 x 5 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 735 and 854 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(119,21) = HCF(735,119) = HCF(854,735) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 529 > 7, we apply the division lemma to 529 and 7, to get
529 = 7 x 75 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 529 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(529,7) .
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Frequently Asked Questions on HCF of 735, 854, 529 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 735, 854, 529?
Answer: HCF of 735, 854, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 854, 529 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 854, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.