Highest Common Factor of 1941, 7077, 98107 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 1941, 7077, 98107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1941, 7077, 98107 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 1941, 7077, 98107 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 1941, 7077, 98107 is 1.

HCF(1941, 7077, 98107) = 1

HCF of 1941, 7077, 98107 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 1941, 7077, 98107 is 1.

Highest Common Factor of 1941,7077,98107 using Euclid's algorithm

Highest Common Factor of 1941,7077,98107 is 1

Step 1: Since 7077 > 1941, we apply the division lemma to 7077 and 1941, to get

7077 = 1941 x 3 + 1254

Step 2: Since the reminder 1941 ≠ 0, we apply division lemma to 1254 and 1941, to get

1941 = 1254 x 1 + 687

Step 3: We consider the new divisor 1254 and the new remainder 687, and apply the division lemma to get

1254 = 687 x 1 + 567

We consider the new divisor 687 and the new remainder 567,and apply the division lemma to get

687 = 567 x 1 + 120

We consider the new divisor 567 and the new remainder 120,and apply the division lemma to get

567 = 120 x 4 + 87

We consider the new divisor 120 and the new remainder 87,and apply the division lemma to get

120 = 87 x 1 + 33

We consider the new divisor 87 and the new remainder 33,and apply the division lemma to get

87 = 33 x 2 + 21

We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get

33 = 21 x 1 + 12

We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get

21 = 12 x 1 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1941 and 7077 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(87,33) = HCF(120,87) = HCF(567,120) = HCF(687,567) = HCF(1254,687) = HCF(1941,1254) = HCF(7077,1941) .

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

Step 1: Since 98107 > 3, we apply the division lemma to 98107 and 3, to get

98107 = 3 x 32702 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 98107 is 1

Notice that 1 = HCF(3,1) = HCF(98107,3) .

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Frequently Asked Questions on HCF of 1941, 7077, 98107 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 1941, 7077, 98107?

Answer: HCF of 1941, 7077, 98107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1941, 7077, 98107 using Euclid's Algorithm?

Answer: For arbitrary numbers 1941, 7077, 98107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.