Highest Common Factor of 343, 7747, 9375 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 343, 7747, 9375 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 7747, 9375 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 343, 7747, 9375 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 343, 7747, 9375 is 1.

HCF(343, 7747, 9375) = 1

HCF of 343, 7747, 9375 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 343, 7747, 9375 is 1.

Highest Common Factor of 343,7747,9375 using Euclid's algorithm

Highest Common Factor of 343,7747,9375 is 1

Step 1: Since 7747 > 343, we apply the division lemma to 7747 and 343, to get

7747 = 343 x 22 + 201

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 201 and 343, to get

343 = 201 x 1 + 142

Step 3: We consider the new divisor 201 and the new remainder 142, and apply the division lemma to get

201 = 142 x 1 + 59

We consider the new divisor 142 and the new remainder 59,and apply the division lemma to get

142 = 59 x 2 + 24

We consider the new divisor 59 and the new remainder 24,and apply the division lemma to get

59 = 24 x 2 + 11

We consider the new divisor 24 and the new remainder 11,and apply the division lemma to get

24 = 11 x 2 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 343 and 7747 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(59,24) = HCF(142,59) = HCF(201,142) = HCF(343,201) = HCF(7747,343) .

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

Step 1: Since 9375 > 1, we apply the division lemma to 9375 and 1, to get

9375 = 1 x 9375 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9375 is 1

Notice that 1 = HCF(9375,1) .

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Frequently Asked Questions on HCF of 343, 7747, 9375 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 343, 7747, 9375?

Answer: HCF of 343, 7747, 9375 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 7747, 9375 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 7747, 9375 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.