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 682, 657, 105, 337 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 682, 657, 105, 337 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 682, 657, 105, 337 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 682, 657, 105, 337 is 1.
HCF(682, 657, 105, 337) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 682, 657, 105, 337 is 1.
Step 1: Since 682 > 657, we apply the division lemma to 682 and 657, to get
682 = 657 x 1 + 25
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 25 and 657, to get
657 = 25 x 26 + 7
Step 3: We consider the new divisor 25 and the new remainder 7, and apply the division lemma to get
25 = 7 x 3 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 682 and 657 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(25,7) = HCF(657,25) = HCF(682,657) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 337 > 1, we apply the division lemma to 337 and 1, to get
337 = 1 x 337 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 337 is 1
Notice that 1 = HCF(337,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 682, 657, 105, 337?
Answer: HCF of 682, 657, 105, 337 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 682, 657, 105, 337 using Euclid's Algorithm?
Answer: For arbitrary numbers 682, 657, 105, 337 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.