Highest Common Factor of 969, 624, 320 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 969, 624, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 969, 624, 320 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 969, 624, 320 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 969, 624, 320 is 1.

HCF(969, 624, 320) = 1

HCF of 969, 624, 320 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 969, 624, 320 is 1.

Highest Common Factor of 969,624,320 using Euclid's algorithm

Highest Common Factor of 969,624,320 is 1

Step 1: Since 969 > 624, we apply the division lemma to 969 and 624, to get

969 = 624 x 1 + 345

Step 2: Since the reminder 624 ≠ 0, we apply division lemma to 345 and 624, to get

624 = 345 x 1 + 279

Step 3: We consider the new divisor 345 and the new remainder 279, and apply the division lemma to get

345 = 279 x 1 + 66

We consider the new divisor 279 and the new remainder 66,and apply the division lemma to get

279 = 66 x 4 + 15

We consider the new divisor 66 and the new remainder 15,and apply the division lemma to get

66 = 15 x 4 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 969 and 624 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(66,15) = HCF(279,66) = HCF(345,279) = HCF(624,345) = HCF(969,624) .

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

Step 1: Since 320 > 3, we apply the division lemma to 320 and 3, to get

320 = 3 x 106 + 2

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

3 = 2 x 1 + 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 3 and 320 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(320,3) .

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Frequently Asked Questions on HCF of 969, 624, 320 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 969, 624, 320?

Answer: HCF of 969, 624, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 969, 624, 320 using Euclid's Algorithm?

Answer: For arbitrary numbers 969, 624, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.