Highest Common Factor of 107, 203, 852 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 107, 203, 852 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 107, 203, 852 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 107, 203, 852 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 107, 203, 852 is 1.

HCF(107, 203, 852) = 1

HCF of 107, 203, 852 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 107, 203, 852 is 1.

Highest Common Factor of 107,203,852 using Euclid's algorithm

Highest Common Factor of 107,203,852 is 1

Step 1: Since 203 > 107, we apply the division lemma to 203 and 107, to get

203 = 107 x 1 + 96

Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 96 and 107, to get

107 = 96 x 1 + 11

Step 3: We consider the new divisor 96 and the new remainder 11, and apply the division lemma to get

96 = 11 x 8 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 107 and 203 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(96,11) = HCF(107,96) = HCF(203,107) .

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

Step 1: Since 852 > 1, we apply the division lemma to 852 and 1, to get

852 = 1 x 852 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 852 is 1

Notice that 1 = HCF(852,1) .

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Frequently Asked Questions on HCF of 107, 203, 852 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 107, 203, 852?

Answer: HCF of 107, 203, 852 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 107, 203, 852 using Euclid's Algorithm?

Answer: For arbitrary numbers 107, 203, 852 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.