Highest Common Factor of 676, 706, 309 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 676, 706, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 676, 706, 309 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 676, 706, 309 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 676, 706, 309 is 1.
HCF(676, 706, 309) = 1
HCF of 676, 706, 309 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 676, 706, 309 is 1.
Highest Common Factor of 676,706,309 is 1
Step 1: Since 706 > 676, we apply the division lemma to 706 and 676, to get
706 = 676 x 1 + 30
Step 2: Since the reminder 676 ≠ 0, we apply division lemma to 30 and 676, to get
676 = 30 x 22 + 16
Step 3: We consider the new divisor 30 and the new remainder 16, and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 676 and 706 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(676,30) = HCF(706,676) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 2, we apply the division lemma to 309 and 2, to get
309 = 2 x 154 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 309 is 1
Notice that 1 = HCF(2,1) = HCF(309,2) .
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Frequently Asked Questions on HCF of 676, 706, 309 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 676, 706, 309?
Answer: HCF of 676, 706, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 676, 706, 309 using Euclid's Algorithm?
Answer: For arbitrary numbers 676, 706, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.