Highest Common Factor of 658, 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 658, 917 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 917 is 7 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 658, 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 658, 917 is 7.
HCF(658, 917) = 7
HCF of 658, 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 658, 917 is 7.
Highest Common Factor of 658,917 is 7
Step 1: Since 917 > 658, we apply the division lemma to 917 and 658, to get
917 = 658 x 1 + 259
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 259 and 658, to get
658 = 259 x 2 + 140
Step 3: We consider the new divisor 259 and the new remainder 140, and apply the division lemma to get
259 = 140 x 1 + 119
We consider the new divisor 140 and the new remainder 119,and apply the division lemma to get
140 = 119 x 1 + 21
We consider the new divisor 119 and the new remainder 21,and apply the division lemma to get
119 = 21 x 5 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 658 and 917 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(119,21) = HCF(140,119) = HCF(259,140) = HCF(658,259) = HCF(917,658) .
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Frequently Asked Questions on HCF of 658, 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 658, 917?
Answer: HCF of 658, 917 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 917 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 917 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.