Highest Common Factor of 945, 3672, 9901 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 945, 3672, 9901 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 945, 3672, 9901 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 945, 3672, 9901 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 945, 3672, 9901 is 1.

HCF(945, 3672, 9901) = 1

HCF of 945, 3672, 9901 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 945, 3672, 9901 is 1.

Highest Common Factor of 945,3672,9901 using Euclid's algorithm

Highest Common Factor of 945,3672,9901 is 1

Step 1: Since 3672 > 945, we apply the division lemma to 3672 and 945, to get

3672 = 945 x 3 + 837

Step 2: Since the reminder 945 ≠ 0, we apply division lemma to 837 and 945, to get

945 = 837 x 1 + 108

Step 3: We consider the new divisor 837 and the new remainder 108, and apply the division lemma to get

837 = 108 x 7 + 81

We consider the new divisor 108 and the new remainder 81,and apply the division lemma to get

108 = 81 x 1 + 27

We consider the new divisor 81 and the new remainder 27,and apply the division lemma to get

81 = 27 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 945 and 3672 is 27

Notice that 27 = HCF(81,27) = HCF(108,81) = HCF(837,108) = HCF(945,837) = HCF(3672,945) .

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

Step 1: Since 9901 > 27, we apply the division lemma to 9901 and 27, to get

9901 = 27 x 366 + 19

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 19 and 27, to get

27 = 19 x 1 + 8

Step 3: We consider the new divisor 19 and the new remainder 8, and apply the division lemma to get

19 = 8 x 2 + 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 27 and 9901 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(9901,27) .

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Frequently Asked Questions on HCF of 945, 3672, 9901 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 945, 3672, 9901?

Answer: HCF of 945, 3672, 9901 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 945, 3672, 9901 using Euclid's Algorithm?

Answer: For arbitrary numbers 945, 3672, 9901 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.