Highest Common Factor of 6424, 7768, 42885 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 6424, 7768, 42885 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6424, 7768, 42885 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 6424, 7768, 42885 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 6424, 7768, 42885 is 1.
HCF(6424, 7768, 42885) = 1
HCF of 6424, 7768, 42885 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6424, 7768, 42885 is 1.
Highest Common Factor of 6424,7768,42885 is 1
Step 1: Since 7768 > 6424, we apply the division lemma to 7768 and 6424, to get
7768 = 6424 x 1 + 1344
Step 2: Since the reminder 6424 ≠ 0, we apply division lemma to 1344 and 6424, to get
6424 = 1344 x 4 + 1048
Step 3: We consider the new divisor 1344 and the new remainder 1048, and apply the division lemma to get
1344 = 1048 x 1 + 296
We consider the new divisor 1048 and the new remainder 296,and apply the division lemma to get
1048 = 296 x 3 + 160
We consider the new divisor 296 and the new remainder 160,and apply the division lemma to get
296 = 160 x 1 + 136
We consider the new divisor 160 and the new remainder 136,and apply the division lemma to get
160 = 136 x 1 + 24
We consider the new divisor 136 and the new remainder 24,and apply the division lemma to get
136 = 24 x 5 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 6424 and 7768 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(136,24) = HCF(160,136) = HCF(296,160) = HCF(1048,296) = HCF(1344,1048) = HCF(6424,1344) = HCF(7768,6424) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42885 > 8, we apply the division lemma to 42885 and 8, to get
42885 = 8 x 5360 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 3: We consider the new divisor 5 and the new remainder 3, and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 8 and 42885 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(42885,8) .
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Frequently Asked Questions on HCF of 6424, 7768, 42885 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 6424, 7768, 42885?
Answer: HCF of 6424, 7768, 42885 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6424, 7768, 42885 using Euclid's Algorithm?
Answer: For arbitrary numbers 6424, 7768, 42885 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.