Highest Common Factor of 710, 994, 917 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 710, 994, 917 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 710, 994, 917 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 710, 994, 917 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 710, 994, 917 is 1.
HCF(710, 994, 917) = 1
HCF of 710, 994, 917 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 710, 994, 917 is 1.
Highest Common Factor of 710,994,917 is 1
Step 1: Since 994 > 710, we apply the division lemma to 994 and 710, to get
994 = 710 x 1 + 284
Step 2: Since the reminder 710 ≠ 0, we apply division lemma to 284 and 710, to get
710 = 284 x 2 + 142
Step 3: We consider the new divisor 284 and the new remainder 142, and apply the division lemma to get
284 = 142 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 142, the HCF of 710 and 994 is 142
Notice that 142 = HCF(284,142) = HCF(710,284) = HCF(994,710) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 917 > 142, we apply the division lemma to 917 and 142, to get
917 = 142 x 6 + 65
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 65 and 142, to get
142 = 65 x 2 + 12
Step 3: We consider the new divisor 65 and the new remainder 12, and apply the division lemma to get
65 = 12 x 5 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 142 and 917 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(65,12) = HCF(142,65) = HCF(917,142) .
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Frequently Asked Questions on HCF of 710, 994, 917 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 710, 994, 917?
Answer: HCF of 710, 994, 917 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 710, 994, 917 using Euclid's Algorithm?
Answer: For arbitrary numbers 710, 994, 917 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.