Highest Common Factor of 9985, 4525, 74132 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 9985, 4525, 74132 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9985, 4525, 74132 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 9985, 4525, 74132 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 9985, 4525, 74132 is 1.

HCF(9985, 4525, 74132) = 1

HCF of 9985, 4525, 74132 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 9985, 4525, 74132 is 1.

Highest Common Factor of 9985,4525,74132 using Euclid's algorithm

Highest Common Factor of 9985,4525,74132 is 1

Step 1: Since 9985 > 4525, we apply the division lemma to 9985 and 4525, to get

9985 = 4525 x 2 + 935

Step 2: Since the reminder 4525 ≠ 0, we apply division lemma to 935 and 4525, to get

4525 = 935 x 4 + 785

Step 3: We consider the new divisor 935 and the new remainder 785, and apply the division lemma to get

935 = 785 x 1 + 150

We consider the new divisor 785 and the new remainder 150,and apply the division lemma to get

785 = 150 x 5 + 35

We consider the new divisor 150 and the new remainder 35,and apply the division lemma to get

150 = 35 x 4 + 10

We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 9985 and 4525 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(150,35) = HCF(785,150) = HCF(935,785) = HCF(4525,935) = HCF(9985,4525) .

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

Step 1: Since 74132 > 5, we apply the division lemma to 74132 and 5, to get

74132 = 5 x 14826 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: 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 5 and 74132 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(74132,5) .

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Frequently Asked Questions on HCF of 9985, 4525, 74132 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 9985, 4525, 74132?

Answer: HCF of 9985, 4525, 74132 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9985, 4525, 74132 using Euclid's Algorithm?

Answer: For arbitrary numbers 9985, 4525, 74132 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.