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 631, 4157, 7321 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 631, 4157, 7321 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 631, 4157, 7321 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 631, 4157, 7321 is 1.
HCF(631, 4157, 7321) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 631, 4157, 7321 is 1.
Step 1: Since 4157 > 631, we apply the division lemma to 4157 and 631, to get
4157 = 631 x 6 + 371
Step 2: Since the reminder 631 ≠ 0, we apply division lemma to 371 and 631, to get
631 = 371 x 1 + 260
Step 3: We consider the new divisor 371 and the new remainder 260, and apply the division lemma to get
371 = 260 x 1 + 111
We consider the new divisor 260 and the new remainder 111,and apply the division lemma to get
260 = 111 x 2 + 38
We consider the new divisor 111 and the new remainder 38,and apply the division lemma to get
111 = 38 x 2 + 35
We consider the new divisor 38 and the new remainder 35,and apply the division lemma to get
38 = 35 x 1 + 3
We consider the new divisor 35 and the new remainder 3,and apply the division lemma to get
35 = 3 x 11 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 631 and 4157 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(35,3) = HCF(38,35) = HCF(111,38) = HCF(260,111) = HCF(371,260) = HCF(631,371) = HCF(4157,631) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7321 > 1, we apply the division lemma to 7321 and 1, to get
7321 = 1 x 7321 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7321 is 1
Notice that 1 = HCF(7321,1) .
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 631, 4157, 7321?
Answer: HCF of 631, 4157, 7321 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 631, 4157, 7321 using Euclid's Algorithm?
Answer: For arbitrary numbers 631, 4157, 7321 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.