Highest Common Factor of 930, 668, 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 930, 668, 991 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 930, 668, 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 930, 668, 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 930, 668, 991 is 1.

HCF(930, 668, 991) = 1

HCF of 930, 668, 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 930, 668, 991 is 1.

Highest Common Factor of 930,668,991 using Euclid's algorithm

Highest Common Factor of 930,668,991 is 1

Step 1: Since 930 > 668, we apply the division lemma to 930 and 668, to get

930 = 668 x 1 + 262

Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 262 and 668, to get

668 = 262 x 2 + 144

Step 3: We consider the new divisor 262 and the new remainder 144, and apply the division lemma to get

262 = 144 x 1 + 118

We consider the new divisor 144 and the new remainder 118,and apply the division lemma to get

144 = 118 x 1 + 26

We consider the new divisor 118 and the new remainder 26,and apply the division lemma to get

118 = 26 x 4 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 930 and 668 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(118,26) = HCF(144,118) = HCF(262,144) = HCF(668,262) = HCF(930,668) .

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

Step 1: Since 991 > 2, we apply the division lemma to 991 and 2, to get

991 = 2 x 495 + 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 991 is 1

Notice that 1 = HCF(2,1) = HCF(991,2) .

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Frequently Asked Questions on HCF of 930, 668, 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 930, 668, 991?

Answer: HCF of 930, 668, 991 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 930, 668, 991 using Euclid's Algorithm?

Answer: For arbitrary numbers 930, 668, 991 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.