Highest Common Factor of 657, 699, 614 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 657, 699, 614 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 699, 614 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 657, 699, 614 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 657, 699, 614 is 1.
HCF(657, 699, 614) = 1
HCF of 657, 699, 614 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 657, 699, 614 is 1.
Highest Common Factor of 657,699,614 is 1
Step 1: Since 699 > 657, we apply the division lemma to 699 and 657, to get
699 = 657 x 1 + 42
Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 42 and 657, to get
657 = 42 x 15 + 27
Step 3: We consider the new divisor 42 and the new remainder 27, and apply the division lemma to get
42 = 27 x 1 + 15
We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get
27 = 15 x 1 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 657 and 699 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(42,27) = HCF(657,42) = HCF(699,657) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 614 > 3, we apply the division lemma to 614 and 3, to get
614 = 3 x 204 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 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 3 and 614 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(614,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 657, 699, 614 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 657, 699, 614?
Answer: HCF of 657, 699, 614 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 699, 614 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 699, 614 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.