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 6391, 7285, 61884 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6391, 7285, 61884 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 6391, 7285, 61884 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 6391, 7285, 61884 is 1.
HCF(6391, 7285, 61884) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6391, 7285, 61884 is 1.
Step 1: Since 7285 > 6391, we apply the division lemma to 7285 and 6391, to get
7285 = 6391 x 1 + 894
Step 2: Since the reminder 6391 ≠ 0, we apply division lemma to 894 and 6391, to get
6391 = 894 x 7 + 133
Step 3: We consider the new divisor 894 and the new remainder 133, and apply the division lemma to get
894 = 133 x 6 + 96
We consider the new divisor 133 and the new remainder 96,and apply the division lemma to get
133 = 96 x 1 + 37
We consider the new divisor 96 and the new remainder 37,and apply the division lemma to get
96 = 37 x 2 + 22
We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get
37 = 22 x 1 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6391 and 7285 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(96,37) = HCF(133,96) = HCF(894,133) = HCF(6391,894) = HCF(7285,6391) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 61884 > 1, we apply the division lemma to 61884 and 1, to get
61884 = 1 x 61884 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 61884 is 1
Notice that 1 = HCF(61884,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 6391, 7285, 61884?
Answer: HCF of 6391, 7285, 61884 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6391, 7285, 61884 using Euclid's Algorithm?
Answer: For arbitrary numbers 6391, 7285, 61884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.