Highest Common Factor of 658, 3115 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, 3115 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 3115 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, 3115 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, 3115 is 7.
HCF(658, 3115) = 7
HCF of 658, 3115 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, 3115 is 7.
Highest Common Factor of 658,3115 is 7
Step 1: Since 3115 > 658, we apply the division lemma to 3115 and 658, to get
3115 = 658 x 4 + 483
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 483 and 658, to get
658 = 483 x 1 + 175
Step 3: We consider the new divisor 483 and the new remainder 175, and apply the division lemma to get
483 = 175 x 2 + 133
We consider the new divisor 175 and the new remainder 133,and apply the division lemma to get
175 = 133 x 1 + 42
We consider the new divisor 133 and the new remainder 42,and apply the division lemma to get
133 = 42 x 3 + 7
We consider the new divisor 42 and the new remainder 7,and apply the division lemma to get
42 = 7 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 658 and 3115 is 7
Notice that 7 = HCF(42,7) = HCF(133,42) = HCF(175,133) = HCF(483,175) = HCF(658,483) = HCF(3115,658) .
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Frequently Asked Questions on HCF of 658, 3115 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, 3115?
Answer: HCF of 658, 3115 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 3115 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 3115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.