Highest Common Factor of 735, 516, 829 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, 516, 829 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 735, 516, 829 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, 516, 829 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, 516, 829 is 1.
HCF(735, 516, 829) = 1
HCF of 735, 516, 829 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, 516, 829 is 1.
Highest Common Factor of 735,516,829 is 1
Step 1: Since 735 > 516, we apply the division lemma to 735 and 516, to get
735 = 516 x 1 + 219
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 219 and 516, to get
516 = 219 x 2 + 78
Step 3: We consider the new divisor 219 and the new remainder 78, and apply the division lemma to get
219 = 78 x 2 + 63
We consider the new divisor 78 and the new remainder 63,and apply the division lemma to get
78 = 63 x 1 + 15
We consider the new divisor 63 and the new remainder 15,and apply the division lemma to get
63 = 15 x 4 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 735 and 516 is 3
Notice that 3 = HCF(15,3) = HCF(63,15) = HCF(78,63) = HCF(219,78) = HCF(516,219) = HCF(735,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 829 > 3, we apply the division lemma to 829 and 3, to get
829 = 3 x 276 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 829 is 1
Notice that 1 = HCF(3,1) = HCF(829,3) .
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Frequently Asked Questions on HCF of 735, 516, 829 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, 516, 829?
Answer: HCF of 735, 516, 829 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 735, 516, 829 using Euclid's Algorithm?
Answer: For arbitrary numbers 735, 516, 829 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.