Highest Common Factor of 680, 373, 659 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 680, 373, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 373, 659 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 680, 373, 659 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 680, 373, 659 is 1.
HCF(680, 373, 659) = 1
HCF of 680, 373, 659 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 680, 373, 659 is 1.
Highest Common Factor of 680,373,659 is 1
Step 1: Since 680 > 373, we apply the division lemma to 680 and 373, to get
680 = 373 x 1 + 307
Step 2: Since the reminder 373 ≠ 0, we apply division lemma to 307 and 373, to get
373 = 307 x 1 + 66
Step 3: We consider the new divisor 307 and the new remainder 66, and apply the division lemma to get
307 = 66 x 4 + 43
We consider the new divisor 66 and the new remainder 43,and apply the division lemma to get
66 = 43 x 1 + 23
We consider the new divisor 43 and the new remainder 23,and apply the division lemma to get
43 = 23 x 1 + 20
We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get
23 = 20 x 1 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 680 and 373 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(66,43) = HCF(307,66) = HCF(373,307) = HCF(680,373) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 659 > 1, we apply the division lemma to 659 and 1, to get
659 = 1 x 659 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 659 is 1
Notice that 1 = HCF(659,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 680, 373, 659 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 680, 373, 659?
Answer: HCF of 680, 373, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 373, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 373, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
