Highest Common Factor of 1972, 8431 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 1972, 8431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1972, 8431 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 1972, 8431 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 1972, 8431 is 1.

HCF(1972, 8431) = 1

HCF of 1972, 8431 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 1972, 8431 is 1.

Highest Common Factor of 1972,8431 using Euclid's algorithm

Highest Common Factor of 1972,8431 is 1

Step 1: Since 8431 > 1972, we apply the division lemma to 8431 and 1972, to get

8431 = 1972 x 4 + 543

Step 2: Since the reminder 1972 ≠ 0, we apply division lemma to 543 and 1972, to get

1972 = 543 x 3 + 343

Step 3: We consider the new divisor 543 and the new remainder 343, and apply the division lemma to get

543 = 343 x 1 + 200

We consider the new divisor 343 and the new remainder 200,and apply the division lemma to get

343 = 200 x 1 + 143

We consider the new divisor 200 and the new remainder 143,and apply the division lemma to get

200 = 143 x 1 + 57

We consider the new divisor 143 and the new remainder 57,and apply the division lemma to get

143 = 57 x 2 + 29

We consider the new divisor 57 and the new remainder 29,and apply the division lemma to get

57 = 29 x 1 + 28

We consider the new divisor 29 and the new remainder 28,and apply the division lemma to get

29 = 28 x 1 + 1

We consider the new divisor 28 and the new remainder 1,and apply the division lemma to get

28 = 1 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1972 and 8431 is 1

Notice that 1 = HCF(28,1) = HCF(29,28) = HCF(57,29) = HCF(143,57) = HCF(200,143) = HCF(343,200) = HCF(543,343) = HCF(1972,543) = HCF(8431,1972) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 1972, 8431 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 1972, 8431?

Answer: HCF of 1972, 8431 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1972, 8431 using Euclid's Algorithm?

Answer: For arbitrary numbers 1972, 8431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.