Highest Common Factor of 9030, 6422, 36562 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 9030, 6422, 36562 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9030, 6422, 36562 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 9030, 6422, 36562 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 9030, 6422, 36562 is 2.
HCF(9030, 6422, 36562) = 2
HCF of 9030, 6422, 36562 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9030, 6422, 36562 is 2.
Highest Common Factor of 9030,6422,36562 is 2
Step 1: Since 9030 > 6422, we apply the division lemma to 9030 and 6422, to get
9030 = 6422 x 1 + 2608
Step 2: Since the reminder 6422 ≠ 0, we apply division lemma to 2608 and 6422, to get
6422 = 2608 x 2 + 1206
Step 3: We consider the new divisor 2608 and the new remainder 1206, and apply the division lemma to get
2608 = 1206 x 2 + 196
We consider the new divisor 1206 and the new remainder 196,and apply the division lemma to get
1206 = 196 x 6 + 30
We consider the new divisor 196 and the new remainder 30,and apply the division lemma to get
196 = 30 x 6 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9030 and 6422 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(196,30) = HCF(1206,196) = HCF(2608,1206) = HCF(6422,2608) = HCF(9030,6422) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36562 > 2, we apply the division lemma to 36562 and 2, to get
36562 = 2 x 18281 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 36562 is 2
Notice that 2 = HCF(36562,2) .
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Frequently Asked Questions on HCF of 9030, 6422, 36562 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 9030, 6422, 36562?
Answer: HCF of 9030, 6422, 36562 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9030, 6422, 36562 using Euclid's Algorithm?
Answer: For arbitrary numbers 9030, 6422, 36562 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
