Highest Common Factor of 3575, 8472 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 3575, 8472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 3575, 8472 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 3575, 8472 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 3575, 8472 is 1.

HCF(3575, 8472) = 1

HCF of 3575, 8472 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 3575, 8472 is 1.

Highest Common Factor of 3575,8472 using Euclid's algorithm

Highest Common Factor of 3575,8472 is 1

Step 1: Since 8472 > 3575, we apply the division lemma to 8472 and 3575, to get

8472 = 3575 x 2 + 1322

Step 2: Since the reminder 3575 ≠ 0, we apply division lemma to 1322 and 3575, to get

3575 = 1322 x 2 + 931

Step 3: We consider the new divisor 1322 and the new remainder 931, and apply the division lemma to get

1322 = 931 x 1 + 391

We consider the new divisor 931 and the new remainder 391,and apply the division lemma to get

931 = 391 x 2 + 149

We consider the new divisor 391 and the new remainder 149,and apply the division lemma to get

391 = 149 x 2 + 93

We consider the new divisor 149 and the new remainder 93,and apply the division lemma to get

149 = 93 x 1 + 56

We consider the new divisor 93 and the new remainder 56,and apply the division lemma to get

93 = 56 x 1 + 37

We consider the new divisor 56 and the new remainder 37,and apply the division lemma to get

56 = 37 x 1 + 19

We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get

37 = 19 x 1 + 18

We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get

19 = 18 x 1 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3575 and 8472 is 1

Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(56,37) = HCF(93,56) = HCF(149,93) = HCF(391,149) = HCF(931,391) = HCF(1322,931) = HCF(3575,1322) = HCF(8472,3575) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 3575, 8472 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 3575, 8472?

Answer: HCF of 3575, 8472 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 3575, 8472 using Euclid's Algorithm?

Answer: For arbitrary numbers 3575, 8472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.