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 637, 504, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 637, 504, 381 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 637, 504, 381 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 637, 504, 381 is 1.
HCF(637, 504, 381) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 637, 504, 381 is 1.
Step 1: Since 637 > 504, we apply the division lemma to 637 and 504, to get
637 = 504 x 1 + 133
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 133 and 504, to get
504 = 133 x 3 + 105
Step 3: We consider the new divisor 133 and the new remainder 105, and apply the division lemma to get
133 = 105 x 1 + 28
We consider the new divisor 105 and the new remainder 28,and apply the division lemma to get
105 = 28 x 3 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 637 and 504 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(105,28) = HCF(133,105) = HCF(504,133) = HCF(637,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 381 > 7, we apply the division lemma to 381 and 7, to get
381 = 7 x 54 + 3
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 3 and 7, to get
7 = 3 x 2 + 1
Step 3: 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 7 and 381 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(381,7) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 637, 504, 381?
Answer: HCF of 637, 504, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 637, 504, 381 using Euclid's Algorithm?
Answer: For arbitrary numbers 637, 504, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.