Highest Common Factor of 851, 600, 307 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 851, 600, 307 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 851, 600, 307 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 851, 600, 307 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 851, 600, 307 is 1.

HCF(851, 600, 307) = 1

HCF of 851, 600, 307 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 851, 600, 307 is 1.

Highest Common Factor of 851,600,307 using Euclid's algorithm

Highest Common Factor of 851,600,307 is 1

Step 1: Since 851 > 600, we apply the division lemma to 851 and 600, to get

851 = 600 x 1 + 251

Step 2: Since the reminder 600 ≠ 0, we apply division lemma to 251 and 600, to get

600 = 251 x 2 + 98

Step 3: We consider the new divisor 251 and the new remainder 98, and apply the division lemma to get

251 = 98 x 2 + 55

We consider the new divisor 98 and the new remainder 55,and apply the division lemma to get

98 = 55 x 1 + 43

We consider the new divisor 55 and the new remainder 43,and apply the division lemma to get

55 = 43 x 1 + 12

We consider the new divisor 43 and the new remainder 12,and apply the division lemma to get

43 = 12 x 3 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 851 and 600 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(55,43) = HCF(98,55) = HCF(251,98) = HCF(600,251) = HCF(851,600) .

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

Step 1: Since 307 > 1, we apply the division lemma to 307 and 1, to get

307 = 1 x 307 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 307 is 1

Notice that 1 = HCF(307,1) .

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Frequently Asked Questions on HCF of 851, 600, 307 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 851, 600, 307?

Answer: HCF of 851, 600, 307 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 851, 600, 307 using Euclid's Algorithm?

Answer: For arbitrary numbers 851, 600, 307 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.