Highest Common Factor of 584, 969, 32 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 584, 969, 32 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 584, 969, 32 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 584, 969, 32 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 584, 969, 32 is 1.

HCF(584, 969, 32) = 1

HCF of 584, 969, 32 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 584, 969, 32 is 1.

Highest Common Factor of 584,969,32 using Euclid's algorithm

Highest Common Factor of 584,969,32 is 1

Step 1: Since 969 > 584, we apply the division lemma to 969 and 584, to get

969 = 584 x 1 + 385

Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 385 and 584, to get

584 = 385 x 1 + 199

Step 3: We consider the new divisor 385 and the new remainder 199, and apply the division lemma to get

385 = 199 x 1 + 186

We consider the new divisor 199 and the new remainder 186,and apply the division lemma to get

199 = 186 x 1 + 13

We consider the new divisor 186 and the new remainder 13,and apply the division lemma to get

186 = 13 x 14 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 584 and 969 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(186,13) = HCF(199,186) = HCF(385,199) = HCF(584,385) = HCF(969,584) .

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

Step 1: Since 32 > 1, we apply the division lemma to 32 and 1, to get

32 = 1 x 32 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32 is 1

Notice that 1 = HCF(32,1) .

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Frequently Asked Questions on HCF of 584, 969, 32 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 584, 969, 32?

Answer: HCF of 584, 969, 32 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 584, 969, 32 using Euclid's Algorithm?

Answer: For arbitrary numbers 584, 969, 32 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.