Highest Common Factor of 262, 614, 374 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 262, 614, 374 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 262, 614, 374 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 262, 614, 374 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 262, 614, 374 is 2.
HCF(262, 614, 374) = 2
HCF of 262, 614, 374 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 262, 614, 374 is 2.
Highest Common Factor of 262,614,374 is 2
Step 1: Since 614 > 262, we apply the division lemma to 614 and 262, to get
614 = 262 x 2 + 90
Step 2: Since the reminder 262 ≠ 0, we apply division lemma to 90 and 262, to get
262 = 90 x 2 + 82
Step 3: We consider the new divisor 90 and the new remainder 82, and apply the division lemma to get
90 = 82 x 1 + 8
We consider the new divisor 82 and the new remainder 8,and apply the division lemma to get
82 = 8 x 10 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 262 and 614 is 2
Notice that 2 = HCF(8,2) = HCF(82,8) = HCF(90,82) = HCF(262,90) = HCF(614,262) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 374 > 2, we apply the division lemma to 374 and 2, to get
374 = 2 x 187 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 374 is 2
Notice that 2 = HCF(374,2) .
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Frequently Asked Questions on HCF of 262, 614, 374 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 262, 614, 374?
Answer: HCF of 262, 614, 374 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 262, 614, 374 using Euclid's Algorithm?
Answer: For arbitrary numbers 262, 614, 374 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.