Highest Common Factor of 7916, 6486, 18421 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 7916, 6486, 18421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7916, 6486, 18421 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 7916, 6486, 18421 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 7916, 6486, 18421 is 1.
HCF(7916, 6486, 18421) = 1
HCF of 7916, 6486, 18421 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7916, 6486, 18421 is 1.
Highest Common Factor of 7916,6486,18421 is 1
Step 1: Since 7916 > 6486, we apply the division lemma to 7916 and 6486, to get
7916 = 6486 x 1 + 1430
Step 2: Since the reminder 6486 ≠ 0, we apply division lemma to 1430 and 6486, to get
6486 = 1430 x 4 + 766
Step 3: We consider the new divisor 1430 and the new remainder 766, and apply the division lemma to get
1430 = 766 x 1 + 664
We consider the new divisor 766 and the new remainder 664,and apply the division lemma to get
766 = 664 x 1 + 102
We consider the new divisor 664 and the new remainder 102,and apply the division lemma to get
664 = 102 x 6 + 52
We consider the new divisor 102 and the new remainder 52,and apply the division lemma to get
102 = 52 x 1 + 50
We consider the new divisor 52 and the new remainder 50,and apply the division lemma to get
52 = 50 x 1 + 2
We consider the new divisor 50 and the new remainder 2,and apply the division lemma to get
50 = 2 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7916 and 6486 is 2
Notice that 2 = HCF(50,2) = HCF(52,50) = HCF(102,52) = HCF(664,102) = HCF(766,664) = HCF(1430,766) = HCF(6486,1430) = HCF(7916,6486) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18421 > 2, we apply the division lemma to 18421 and 2, to get
18421 = 2 x 9210 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 18421 is 1
Notice that 1 = HCF(2,1) = HCF(18421,2) .
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Frequently Asked Questions on HCF of 7916, 6486, 18421 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 7916, 6486, 18421?
Answer: HCF of 7916, 6486, 18421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7916, 6486, 18421 using Euclid's Algorithm?
Answer: For arbitrary numbers 7916, 6486, 18421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.