Highest Common Factor of 641, 7523, 8407 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 641, 7523, 8407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 641, 7523, 8407 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 641, 7523, 8407 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 641, 7523, 8407 is 1.

HCF(641, 7523, 8407) = 1

HCF of 641, 7523, 8407 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 641, 7523, 8407 is 1.

Highest Common Factor of 641,7523,8407 using Euclid's algorithm

Highest Common Factor of 641,7523,8407 is 1

Step 1: Since 7523 > 641, we apply the division lemma to 7523 and 641, to get

7523 = 641 x 11 + 472

Step 2: Since the reminder 641 ≠ 0, we apply division lemma to 472 and 641, to get

641 = 472 x 1 + 169

Step 3: We consider the new divisor 472 and the new remainder 169, and apply the division lemma to get

472 = 169 x 2 + 134

We consider the new divisor 169 and the new remainder 134,and apply the division lemma to get

169 = 134 x 1 + 35

We consider the new divisor 134 and the new remainder 35,and apply the division lemma to get

134 = 35 x 3 + 29

We consider the new divisor 35 and the new remainder 29,and apply the division lemma to get

35 = 29 x 1 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 641 and 7523 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(35,29) = HCF(134,35) = HCF(169,134) = HCF(472,169) = HCF(641,472) = HCF(7523,641) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 8407 > 1, we apply the division lemma to 8407 and 1, to get

8407 = 1 x 8407 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8407 is 1

Notice that 1 = HCF(8407,1) .

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Frequently Asked Questions on HCF of 641, 7523, 8407 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 641, 7523, 8407?

Answer: HCF of 641, 7523, 8407 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 641, 7523, 8407 using Euclid's Algorithm?

Answer: For arbitrary numbers 641, 7523, 8407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.