Highest Common Factor of 8354, 7125 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 8354, 7125 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8354, 7125 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 8354, 7125 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 8354, 7125 is 1.

HCF(8354, 7125) = 1

HCF of 8354, 7125 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 8354, 7125 is 1.

Highest Common Factor of 8354,7125 using Euclid's algorithm

Highest Common Factor of 8354,7125 is 1

Step 1: Since 8354 > 7125, we apply the division lemma to 8354 and 7125, to get

8354 = 7125 x 1 + 1229

Step 2: Since the reminder 7125 ≠ 0, we apply division lemma to 1229 and 7125, to get

7125 = 1229 x 5 + 980

Step 3: We consider the new divisor 1229 and the new remainder 980, and apply the division lemma to get

1229 = 980 x 1 + 249

We consider the new divisor 980 and the new remainder 249,and apply the division lemma to get

980 = 249 x 3 + 233

We consider the new divisor 249 and the new remainder 233,and apply the division lemma to get

249 = 233 x 1 + 16

We consider the new divisor 233 and the new remainder 16,and apply the division lemma to get

233 = 16 x 14 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 8354 and 7125 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(233,16) = HCF(249,233) = HCF(980,249) = HCF(1229,980) = HCF(7125,1229) = HCF(8354,7125) .

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Frequently Asked Questions on HCF of 8354, 7125 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 8354, 7125?

Answer: HCF of 8354, 7125 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8354, 7125 using Euclid's Algorithm?

Answer: For arbitrary numbers 8354, 7125 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.