Highest Common Factor of 976, 690, 557, 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 976, 690, 557, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 976, 690, 557, 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 976, 690, 557, 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 976, 690, 557, 320 is 1.

HCF(976, 690, 557, 320) = 1

HCF of 976, 690, 557, 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 976, 690, 557, 320 is 1.

Highest Common Factor of 976,690,557,320 using Euclid's algorithm

Highest Common Factor of 976,690,557,320 is 1

Step 1: Since 976 > 690, we apply the division lemma to 976 and 690, to get

976 = 690 x 1 + 286

Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 286 and 690, to get

690 = 286 x 2 + 118

Step 3: We consider the new divisor 286 and the new remainder 118, and apply the division lemma to get

286 = 118 x 2 + 50

We consider the new divisor 118 and the new remainder 50,and apply the division lemma to get

118 = 50 x 2 + 18

We consider the new divisor 50 and the new remainder 18,and apply the division lemma to get

50 = 18 x 2 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 976 and 690 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(50,18) = HCF(118,50) = HCF(286,118) = HCF(690,286) = HCF(976,690) .

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

Step 1: Since 557 > 2, we apply the division lemma to 557 and 2, to get

557 = 2 x 278 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 557 is 1

Notice that 1 = HCF(2,1) = HCF(557,2) .

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

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

320 = 1 x 320 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 320 is 1

Notice that 1 = HCF(320,1) .

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Frequently Asked Questions on HCF of 976, 690, 557, 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 976, 690, 557, 320?

Answer: HCF of 976, 690, 557, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 976, 690, 557, 320 using Euclid's Algorithm?

Answer: For arbitrary numbers 976, 690, 557, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.