Highest Common Factor of 812, 920, 689 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 812, 920, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 812, 920, 689 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 812, 920, 689 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 812, 920, 689 is 1.
HCF(812, 920, 689) = 1
HCF of 812, 920, 689 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 812, 920, 689 is 1.
Highest Common Factor of 812,920,689 is 1
Step 1: Since 920 > 812, we apply the division lemma to 920 and 812, to get
920 = 812 x 1 + 108
Step 2: Since the reminder 812 ≠ 0, we apply division lemma to 108 and 812, to get
812 = 108 x 7 + 56
Step 3: We consider the new divisor 108 and the new remainder 56, and apply the division lemma to get
108 = 56 x 1 + 52
We consider the new divisor 56 and the new remainder 52,and apply the division lemma to get
56 = 52 x 1 + 4
We consider the new divisor 52 and the new remainder 4,and apply the division lemma to get
52 = 4 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 812 and 920 is 4
Notice that 4 = HCF(52,4) = HCF(56,52) = HCF(108,56) = HCF(812,108) = HCF(920,812) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 689 > 4, we apply the division lemma to 689 and 4, to get
689 = 4 x 172 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 689 is 1
Notice that 1 = HCF(4,1) = HCF(689,4) .
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Frequently Asked Questions on HCF of 812, 920, 689 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 812, 920, 689?
Answer: HCF of 812, 920, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 812, 920, 689 using Euclid's Algorithm?
Answer: For arbitrary numbers 812, 920, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.