Highest Common Factor of 992, 764, 686, 151 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 992, 764, 686, 151 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 992, 764, 686, 151 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 992, 764, 686, 151 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 992, 764, 686, 151 is 1.

HCF(992, 764, 686, 151) = 1

HCF of 992, 764, 686, 151 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 992, 764, 686, 151 is 1.

Highest Common Factor of 992,764,686,151 using Euclid's algorithm

Highest Common Factor of 992,764,686,151 is 1

Step 1: Since 992 > 764, we apply the division lemma to 992 and 764, to get

992 = 764 x 1 + 228

Step 2: Since the reminder 764 ≠ 0, we apply division lemma to 228 and 764, to get

764 = 228 x 3 + 80

Step 3: We consider the new divisor 228 and the new remainder 80, and apply the division lemma to get

228 = 80 x 2 + 68

We consider the new divisor 80 and the new remainder 68,and apply the division lemma to get

80 = 68 x 1 + 12

We consider the new divisor 68 and the new remainder 12,and apply the division lemma to get

68 = 12 x 5 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 992 and 764 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(68,12) = HCF(80,68) = HCF(228,80) = HCF(764,228) = HCF(992,764) .

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

Step 1: Since 686 > 4, we apply the division lemma to 686 and 4, to get

686 = 4 x 171 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 686 is 2

Notice that 2 = HCF(4,2) = HCF(686,4) .

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

Step 1: Since 151 > 2, we apply the division lemma to 151 and 2, to get

151 = 2 x 75 + 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 151 is 1

Notice that 1 = HCF(2,1) = HCF(151,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 992, 764, 686, 151 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 992, 764, 686, 151?

Answer: HCF of 992, 764, 686, 151 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 992, 764, 686, 151 using Euclid's Algorithm?

Answer: For arbitrary numbers 992, 764, 686, 151 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.