Highest Common Factor of 658, 3750 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, 3750 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 3750 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 658, 3750 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, 3750 is 2.
HCF(658, 3750) = 2
HCF of 658, 3750 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, 3750 is 2.
Highest Common Factor of 658,3750 is 2
Step 1: Since 3750 > 658, we apply the division lemma to 3750 and 658, to get
3750 = 658 x 5 + 460
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 460 and 658, to get
658 = 460 x 1 + 198
Step 3: We consider the new divisor 460 and the new remainder 198, and apply the division lemma to get
460 = 198 x 2 + 64
We consider the new divisor 198 and the new remainder 64,and apply the division lemma to get
198 = 64 x 3 + 6
We consider the new divisor 64 and the new remainder 6,and apply the division lemma to get
64 = 6 x 10 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 3750 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(64,6) = HCF(198,64) = HCF(460,198) = HCF(658,460) = HCF(3750,658) .
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Frequently Asked Questions on HCF of 658, 3750 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, 3750?
Answer: HCF of 658, 3750 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 3750 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 3750 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.