Highest Common Factor of 982, 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 982, 414 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 982, 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 982, 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 982, 414 is 2.
HCF(982, 414) = 2
HCF of 982, 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 982, 414 is 2.
Highest Common Factor of 982,414 is 2
Step 1: Since 982 > 414, we apply the division lemma to 982 and 414, to get
982 = 414 x 2 + 154
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 154 and 414, to get
414 = 154 x 2 + 106
Step 3: We consider the new divisor 154 and the new remainder 106, and apply the division lemma to get
154 = 106 x 1 + 48
We consider the new divisor 106 and the new remainder 48,and apply the division lemma to get
106 = 48 x 2 + 10
We consider the new divisor 48 and the new remainder 10,and apply the division lemma to get
48 = 10 x 4 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 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 982 and 414 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(48,10) = HCF(106,48) = HCF(154,106) = HCF(414,154) = HCF(982,414) .
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Frequently Asked Questions on HCF of 982, 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 982, 414?
Answer: HCF of 982, 414 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 982, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 982, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.