Highest Common Factor of 963, 504, 381, 51 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 963, 504, 381, 51 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 963, 504, 381, 51 is 3 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 963, 504, 381, 51 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 963, 504, 381, 51 is 3.
HCF(963, 504, 381, 51) = 3
HCF of 963, 504, 381, 51 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 963, 504, 381, 51 is 3.
Highest Common Factor of 963,504,381,51 is 3
Step 1: Since 963 > 504, we apply the division lemma to 963 and 504, to get
963 = 504 x 1 + 459
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 459 and 504, to get
504 = 459 x 1 + 45
Step 3: We consider the new divisor 459 and the new remainder 45, and apply the division lemma to get
459 = 45 x 10 + 9
We consider the new divisor 45 and the new remainder 9, and apply the division lemma to get
45 = 9 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 963 and 504 is 9
Notice that 9 = HCF(45,9) = HCF(459,45) = HCF(504,459) = HCF(963,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 381 > 9, we apply the division lemma to 381 and 9, to get
381 = 9 x 42 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 381 is 3
Notice that 3 = HCF(9,3) = HCF(381,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51 > 3, we apply the division lemma to 51 and 3, to get
51 = 3 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 51 is 3
Notice that 3 = HCF(51,3) .
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Frequently Asked Questions on HCF of 963, 504, 381, 51 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 963, 504, 381, 51?
Answer: HCF of 963, 504, 381, 51 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 963, 504, 381, 51 using Euclid's Algorithm?
Answer: For arbitrary numbers 963, 504, 381, 51 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.