Highest Common Factor of 832, 688, 810 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 832, 688, 810 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 832, 688, 810 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 832, 688, 810 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 832, 688, 810 is 2.
HCF(832, 688, 810) = 2
HCF of 832, 688, 810 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 832, 688, 810 is 2.
Highest Common Factor of 832,688,810 is 2
Step 1: Since 832 > 688, we apply the division lemma to 832 and 688, to get
832 = 688 x 1 + 144
Step 2: Since the reminder 688 ≠ 0, we apply division lemma to 144 and 688, to get
688 = 144 x 4 + 112
Step 3: We consider the new divisor 144 and the new remainder 112, and apply the division lemma to get
144 = 112 x 1 + 32
We consider the new divisor 112 and the new remainder 32,and apply the division lemma to get
112 = 32 x 3 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 832 and 688 is 16
Notice that 16 = HCF(32,16) = HCF(112,32) = HCF(144,112) = HCF(688,144) = HCF(832,688) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 810 > 16, we apply the division lemma to 810 and 16, to get
810 = 16 x 50 + 10
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 10 and 16, to get
16 = 10 x 1 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 16 and 810 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(810,16) .
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Frequently Asked Questions on HCF of 832, 688, 810 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 832, 688, 810?
Answer: HCF of 832, 688, 810 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 832, 688, 810 using Euclid's Algorithm?
Answer: For arbitrary numbers 832, 688, 810 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.