Highest Common Factor of 665, 3974, 3126 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 665, 3974, 3126 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 3974, 3126 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 665, 3974, 3126 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 665, 3974, 3126 is 1.
HCF(665, 3974, 3126) = 1
HCF of 665, 3974, 3126 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 3974, 3126 is 1.
Highest Common Factor of 665,3974,3126 is 1
Step 1: Since 3974 > 665, we apply the division lemma to 3974 and 665, to get
3974 = 665 x 5 + 649
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 649 and 665, to get
665 = 649 x 1 + 16
Step 3: We consider the new divisor 649 and the new remainder 16, and apply the division lemma to get
649 = 16 x 40 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 665 and 3974 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(649,16) = HCF(665,649) = HCF(3974,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3126 > 1, we apply the division lemma to 3126 and 1, to get
3126 = 1 x 3126 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3126 is 1
Notice that 1 = HCF(3126,1) .
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Frequently Asked Questions on HCF of 665, 3974, 3126 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 665, 3974, 3126?
Answer: HCF of 665, 3974, 3126 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 3974, 3126 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 3974, 3126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.