Highest Common Factor of 917, 378, 680 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 917, 378, 680 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 917, 378, 680 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 917, 378, 680 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 917, 378, 680 is 1.
HCF(917, 378, 680) = 1
HCF of 917, 378, 680 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 917, 378, 680 is 1.
Highest Common Factor of 917,378,680 is 1
Step 1: Since 917 > 378, we apply the division lemma to 917 and 378, to get
917 = 378 x 2 + 161
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 161 and 378, to get
378 = 161 x 2 + 56
Step 3: We consider the new divisor 161 and the new remainder 56, and apply the division lemma to get
161 = 56 x 2 + 49
We consider the new divisor 56 and the new remainder 49,and apply the division lemma to get
56 = 49 x 1 + 7
We consider the new divisor 49 and the new remainder 7,and apply the division lemma to get
49 = 7 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 917 and 378 is 7
Notice that 7 = HCF(49,7) = HCF(56,49) = HCF(161,56) = HCF(378,161) = HCF(917,378) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 7, we apply the division lemma to 680 and 7, to get
680 = 7 x 97 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, 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 7 and 680 is 1
Notice that 1 = HCF(7,1) = HCF(680,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 917, 378, 680 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 917, 378, 680?
Answer: HCF of 917, 378, 680 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 917, 378, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 917, 378, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
