Highest Common Factor of 298, 976, 414 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 298, 976, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 298, 976, 414 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 298, 976, 414 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 298, 976, 414 is 2.
HCF(298, 976, 414) = 2
HCF of 298, 976, 414 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 298, 976, 414 is 2.
Highest Common Factor of 298,976,414 is 2
Step 1: Since 976 > 298, we apply the division lemma to 976 and 298, to get
976 = 298 x 3 + 82
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 82 and 298, to get
298 = 82 x 3 + 52
Step 3: We consider the new divisor 82 and the new remainder 52, and apply the division lemma to get
82 = 52 x 1 + 30
We consider the new divisor 52 and the new remainder 30,and apply the division lemma to get
52 = 30 x 1 + 22
We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get
30 = 22 x 1 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 298 and 976 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(52,30) = HCF(82,52) = HCF(298,82) = HCF(976,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 2, we apply the division lemma to 414 and 2, to get
414 = 2 x 207 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 414 is 2
Notice that 2 = HCF(414,2) .
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Frequently Asked Questions on HCF of 298, 976, 414 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 298, 976, 414?
Answer: HCF of 298, 976, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 298, 976, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 298, 976, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.