Highest Common Factor of 835, 724, 64 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 835, 724, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 835, 724, 64 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 835, 724, 64 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 835, 724, 64 is 1.
HCF(835, 724, 64) = 1
HCF of 835, 724, 64 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 835, 724, 64 is 1.
Highest Common Factor of 835,724,64 is 1
Step 1: Since 835 > 724, we apply the division lemma to 835 and 724, to get
835 = 724 x 1 + 111
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 111 and 724, to get
724 = 111 x 6 + 58
Step 3: We consider the new divisor 111 and the new remainder 58, and apply the division lemma to get
111 = 58 x 1 + 53
We consider the new divisor 58 and the new remainder 53,and apply the division lemma to get
58 = 53 x 1 + 5
We consider the new divisor 53 and the new remainder 5,and apply the division lemma to get
53 = 5 x 10 + 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 835 and 724 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(53,5) = HCF(58,53) = HCF(111,58) = HCF(724,111) = HCF(835,724) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get
64 = 1 x 64 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1
Notice that 1 = HCF(64,1) .
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Frequently Asked Questions on HCF of 835, 724, 64 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 835, 724, 64?
Answer: HCF of 835, 724, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 835, 724, 64 using Euclid's Algorithm?
Answer: For arbitrary numbers 835, 724, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.