Highest Common Factor of 834, 679, 660 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 834, 679, 660 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 834, 679, 660 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 834, 679, 660 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 834, 679, 660 is 1.
HCF(834, 679, 660) = 1
HCF of 834, 679, 660 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 834, 679, 660 is 1.
Highest Common Factor of 834,679,660 is 1
Step 1: Since 834 > 679, we apply the division lemma to 834 and 679, to get
834 = 679 x 1 + 155
Step 2: Since the reminder 679 ≠ 0, we apply division lemma to 155 and 679, to get
679 = 155 x 4 + 59
Step 3: We consider the new divisor 155 and the new remainder 59, and apply the division lemma to get
155 = 59 x 2 + 37
We consider the new divisor 59 and the new remainder 37,and apply the division lemma to get
59 = 37 x 1 + 22
We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get
37 = 22 x 1 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 834 and 679 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(59,37) = HCF(155,59) = HCF(679,155) = HCF(834,679) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get
660 = 1 x 660 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1
Notice that 1 = HCF(660,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 834, 679, 660 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 834, 679, 660?
Answer: HCF of 834, 679, 660 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 834, 679, 660 using Euclid's Algorithm?
Answer: For arbitrary numbers 834, 679, 660 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.