Highest Common Factor of 776, 492, 223, 14 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 776, 492, 223, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 776, 492, 223, 14 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 776, 492, 223, 14 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 776, 492, 223, 14 is 1.

HCF(776, 492, 223, 14) = 1

HCF of 776, 492, 223, 14 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 776, 492, 223, 14 is 1.

Highest Common Factor of 776,492,223,14 using Euclid's algorithm

Highest Common Factor of 776,492,223,14 is 1

Step 1: Since 776 > 492, we apply the division lemma to 776 and 492, to get

776 = 492 x 1 + 284

Step 2: Since the reminder 492 ≠ 0, we apply division lemma to 284 and 492, to get

492 = 284 x 1 + 208

Step 3: We consider the new divisor 284 and the new remainder 208, and apply the division lemma to get

284 = 208 x 1 + 76

We consider the new divisor 208 and the new remainder 76,and apply the division lemma to get

208 = 76 x 2 + 56

We consider the new divisor 76 and the new remainder 56,and apply the division lemma to get

76 = 56 x 1 + 20

We consider the new divisor 56 and the new remainder 20,and apply the division lemma to get

56 = 20 x 2 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 776 and 492 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(56,20) = HCF(76,56) = HCF(208,76) = HCF(284,208) = HCF(492,284) = HCF(776,492) .

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

Step 1: Since 223 > 4, we apply the division lemma to 223 and 4, to get

223 = 4 x 55 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 223 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(223,4) .

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

Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1

Notice that 1 = HCF(14,1) .

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Frequently Asked Questions on HCF of 776, 492, 223, 14 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 776, 492, 223, 14?

Answer: HCF of 776, 492, 223, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 776, 492, 223, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 776, 492, 223, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.