Highest Common Factor of 680, 816, 678 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, 816, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 680, 816, 678 is 2 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, 816, 678 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, 816, 678 is 2.
HCF(680, 816, 678) = 2
HCF of 680, 816, 678 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, 816, 678 is 2.
Highest Common Factor of 680,816,678 is 2
Step 1: Since 816 > 680, we apply the division lemma to 816 and 680, to get
816 = 680 x 1 + 136
Step 2: Since the reminder 680 ≠ 0, we apply division lemma to 136 and 680, to get
680 = 136 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 136, the HCF of 680 and 816 is 136
Notice that 136 = HCF(680,136) = HCF(816,680) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 678 > 136, we apply the division lemma to 678 and 136, to get
678 = 136 x 4 + 134
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 134 and 136, to get
136 = 134 x 1 + 2
Step 3: We consider the new divisor 134 and the new remainder 2, and apply the division lemma to get
134 = 2 x 67 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 136 and 678 is 2
Notice that 2 = HCF(134,2) = HCF(136,134) = HCF(678,136) .
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, 816, 678 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, 816, 678?
Answer: HCF of 680, 816, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 680, 816, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 680, 816, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.