Highest Common Factor of 985, 646, 133 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 985, 646, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 985, 646, 133 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 985, 646, 133 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 985, 646, 133 is 1.

HCF(985, 646, 133) = 1

HCF of 985, 646, 133 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 985, 646, 133 is 1.

Highest Common Factor of 985,646,133 using Euclid's algorithm

Highest Common Factor of 985,646,133 is 1

Step 1: Since 985 > 646, we apply the division lemma to 985 and 646, to get

985 = 646 x 1 + 339

Step 2: Since the reminder 646 ≠ 0, we apply division lemma to 339 and 646, to get

646 = 339 x 1 + 307

Step 3: We consider the new divisor 339 and the new remainder 307, and apply the division lemma to get

339 = 307 x 1 + 32

We consider the new divisor 307 and the new remainder 32,and apply the division lemma to get

307 = 32 x 9 + 19

We consider the new divisor 32 and the new remainder 19,and apply the division lemma to get

32 = 19 x 1 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 985 and 646 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(307,32) = HCF(339,307) = HCF(646,339) = HCF(985,646) .

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

Step 1: Since 133 > 1, we apply the division lemma to 133 and 1, to get

133 = 1 x 133 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 133 is 1

Notice that 1 = HCF(133,1) .

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Frequently Asked Questions on HCF of 985, 646, 133 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 985, 646, 133?

Answer: HCF of 985, 646, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 985, 646, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 985, 646, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.