Highest Common Factor of 960, 520, 991 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 960, 520, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 960, 520, 991 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 960, 520, 991 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 960, 520, 991 is 1.

HCF(960, 520, 991) = 1

HCF of 960, 520, 991 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 960, 520, 991 is 1.

Highest Common Factor of 960,520,991 using Euclid's algorithm

Highest Common Factor of 960,520,991 is 1

Step 1: Since 960 > 520, we apply the division lemma to 960 and 520, to get

960 = 520 x 1 + 440

Step 2: Since the reminder 520 ≠ 0, we apply division lemma to 440 and 520, to get

520 = 440 x 1 + 80

Step 3: We consider the new divisor 440 and the new remainder 80, and apply the division lemma to get

440 = 80 x 5 + 40

We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get

80 = 40 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 960 and 520 is 40

Notice that 40 = HCF(80,40) = HCF(440,80) = HCF(520,440) = HCF(960,520) .

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

Step 1: Since 991 > 40, we apply the division lemma to 991 and 40, to get

991 = 40 x 24 + 31

Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 31 and 40, to get

40 = 31 x 1 + 9

Step 3: We consider the new divisor 31 and the new remainder 9, and apply the division lemma to get

31 = 9 x 3 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 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 40 and 991 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(31,9) = HCF(40,31) = HCF(991,40) .

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Frequently Asked Questions on HCF of 960, 520, 991 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 960, 520, 991?

Answer: HCF of 960, 520, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 960, 520, 991 using Euclid's Algorithm?

Answer: For arbitrary numbers 960, 520, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.