Highest Common Factor of 8922, 3524, 38530 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 8922, 3524, 38530 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8922, 3524, 38530 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 8922, 3524, 38530 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 8922, 3524, 38530 is 2.
HCF(8922, 3524, 38530) = 2
HCF of 8922, 3524, 38530 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8922, 3524, 38530 is 2.
Highest Common Factor of 8922,3524,38530 is 2
Step 1: Since 8922 > 3524, we apply the division lemma to 8922 and 3524, to get
8922 = 3524 x 2 + 1874
Step 2: Since the reminder 3524 ≠ 0, we apply division lemma to 1874 and 3524, to get
3524 = 1874 x 1 + 1650
Step 3: We consider the new divisor 1874 and the new remainder 1650, and apply the division lemma to get
1874 = 1650 x 1 + 224
We consider the new divisor 1650 and the new remainder 224,and apply the division lemma to get
1650 = 224 x 7 + 82
We consider the new divisor 224 and the new remainder 82,and apply the division lemma to get
224 = 82 x 2 + 60
We consider the new divisor 82 and the new remainder 60,and apply the division lemma to get
82 = 60 x 1 + 22
We consider the new divisor 60 and the new remainder 22,and apply the division lemma to get
60 = 22 x 2 + 16
We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get
22 = 16 x 1 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8922 and 3524 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(60,22) = HCF(82,60) = HCF(224,82) = HCF(1650,224) = HCF(1874,1650) = HCF(3524,1874) = HCF(8922,3524) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38530 > 2, we apply the division lemma to 38530 and 2, to get
38530 = 2 x 19265 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 38530 is 2
Notice that 2 = HCF(38530,2) .
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Frequently Asked Questions on HCF of 8922, 3524, 38530 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 8922, 3524, 38530?
Answer: HCF of 8922, 3524, 38530 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8922, 3524, 38530 using Euclid's Algorithm?
Answer: For arbitrary numbers 8922, 3524, 38530 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.