Highest Common Factor of 390, 102, 914 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 390, 102, 914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 390, 102, 914 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 390, 102, 914 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 390, 102, 914 is 2.
HCF(390, 102, 914) = 2
HCF of 390, 102, 914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 390, 102, 914 is 2.
Highest Common Factor of 390,102,914 is 2
Step 1: Since 390 > 102, we apply the division lemma to 390 and 102, to get
390 = 102 x 3 + 84
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 84 and 102, to get
102 = 84 x 1 + 18
Step 3: We consider the new divisor 84 and the new remainder 18, and apply the division lemma to get
84 = 18 x 4 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 390 and 102 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(84,18) = HCF(102,84) = HCF(390,102) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 914 > 6, we apply the division lemma to 914 and 6, to get
914 = 6 x 152 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 914 is 2
Notice that 2 = HCF(6,2) = HCF(914,6) .
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Frequently Asked Questions on HCF of 390, 102, 914 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 390, 102, 914?
Answer: HCF of 390, 102, 914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 390, 102, 914 using Euclid's Algorithm?
Answer: For arbitrary numbers 390, 102, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
