Highest Common Factor of 303, 6624, 2108 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 303, 6624, 2108 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 303, 6624, 2108 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 303, 6624, 2108 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 303, 6624, 2108 is 1.
HCF(303, 6624, 2108) = 1
HCF of 303, 6624, 2108 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 303, 6624, 2108 is 1.
Highest Common Factor of 303,6624,2108 is 1
Step 1: Since 6624 > 303, we apply the division lemma to 6624 and 303, to get
6624 = 303 x 21 + 261
Step 2: Since the reminder 303 ≠ 0, we apply division lemma to 261 and 303, to get
303 = 261 x 1 + 42
Step 3: We consider the new divisor 261 and the new remainder 42, and apply the division lemma to get
261 = 42 x 6 + 9
We consider the new divisor 42 and the new remainder 9,and apply the division lemma to get
42 = 9 x 4 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 303 and 6624 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(42,9) = HCF(261,42) = HCF(303,261) = HCF(6624,303) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2108 > 3, we apply the division lemma to 2108 and 3, to get
2108 = 3 x 702 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 2108 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(2108,3) .
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Frequently Asked Questions on HCF of 303, 6624, 2108 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 303, 6624, 2108?
Answer: HCF of 303, 6624, 2108 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 303, 6624, 2108 using Euclid's Algorithm?
Answer: For arbitrary numbers 303, 6624, 2108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.