Highest Common Factor of 312, 689, 912 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 312, 689, 912 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 689, 912 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 312, 689, 912 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 312, 689, 912 is 1.
HCF(312, 689, 912) = 1
HCF of 312, 689, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 689, 912 is 1.
Highest Common Factor of 312,689,912 is 1
Step 1: Since 689 > 312, we apply the division lemma to 689 and 312, to get
689 = 312 x 2 + 65
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 65 and 312, to get
312 = 65 x 4 + 52
Step 3: We consider the new divisor 65 and the new remainder 52, and apply the division lemma to get
65 = 52 x 1 + 13
We consider the new divisor 52 and the new remainder 13, and apply the division lemma to get
52 = 13 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 312 and 689 is 13
Notice that 13 = HCF(52,13) = HCF(65,52) = HCF(312,65) = HCF(689,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 13, we apply the division lemma to 912 and 13, to get
912 = 13 x 70 + 2
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get
13 = 2 x 6 + 1
Step 3: 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 13 and 912 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(912,13) .
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Frequently Asked Questions on HCF of 312, 689, 912 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 312, 689, 912?
Answer: HCF of 312, 689, 912 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 689, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 689, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.