Highest Common Factor of 8522, 8931, 30300 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 8522, 8931, 30300 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8522, 8931, 30300 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 8522, 8931, 30300 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 8522, 8931, 30300 is 1.
HCF(8522, 8931, 30300) = 1
HCF of 8522, 8931, 30300 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8522, 8931, 30300 is 1.
Highest Common Factor of 8522,8931,30300 is 1
Step 1: Since 8931 > 8522, we apply the division lemma to 8931 and 8522, to get
8931 = 8522 x 1 + 409
Step 2: Since the reminder 8522 ≠ 0, we apply division lemma to 409 and 8522, to get
8522 = 409 x 20 + 342
Step 3: We consider the new divisor 409 and the new remainder 342, and apply the division lemma to get
409 = 342 x 1 + 67
We consider the new divisor 342 and the new remainder 67,and apply the division lemma to get
342 = 67 x 5 + 7
We consider the new divisor 67 and the new remainder 7,and apply the division lemma to get
67 = 7 x 9 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8522 and 8931 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(67,7) = HCF(342,67) = HCF(409,342) = HCF(8522,409) = HCF(8931,8522) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30300 > 1, we apply the division lemma to 30300 and 1, to get
30300 = 1 x 30300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30300 is 1
Notice that 1 = HCF(30300,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8522, 8931, 30300 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 8522, 8931, 30300?
Answer: HCF of 8522, 8931, 30300 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8522, 8931, 30300 using Euclid's Algorithm?
Answer: For arbitrary numbers 8522, 8931, 30300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.