Highest Common Factor of 702, 891, 621, 305 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 702, 891, 621, 305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 702, 891, 621, 305 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 702, 891, 621, 305 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 702, 891, 621, 305 is 1.

HCF(702, 891, 621, 305) = 1

HCF of 702, 891, 621, 305 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 702, 891, 621, 305 is 1.

Highest Common Factor of 702,891,621,305 using Euclid's algorithm

Highest Common Factor of 702,891,621,305 is 1

Step 1: Since 891 > 702, we apply the division lemma to 891 and 702, to get

891 = 702 x 1 + 189

Step 2: Since the reminder 702 ≠ 0, we apply division lemma to 189 and 702, to get

702 = 189 x 3 + 135

Step 3: We consider the new divisor 189 and the new remainder 135, and apply the division lemma to get

189 = 135 x 1 + 54

We consider the new divisor 135 and the new remainder 54,and apply the division lemma to get

135 = 54 x 2 + 27

We consider the new divisor 54 and the new remainder 27,and apply the division lemma to get

54 = 27 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 702 and 891 is 27

Notice that 27 = HCF(54,27) = HCF(135,54) = HCF(189,135) = HCF(702,189) = HCF(891,702) .

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

Step 1: Since 621 > 27, we apply the division lemma to 621 and 27, to get

621 = 27 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 27 and 621 is 27

Notice that 27 = HCF(621,27) .

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

Step 1: Since 305 > 27, we apply the division lemma to 305 and 27, to get

305 = 27 x 11 + 8

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 8 and 27, to get

27 = 8 x 3 + 3

Step 3: We consider the new divisor 8 and the new remainder 3, and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 27 and 305 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(27,8) = HCF(305,27) .

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Frequently Asked Questions on HCF of 702, 891, 621, 305 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 702, 891, 621, 305?

Answer: HCF of 702, 891, 621, 305 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 702, 891, 621, 305 using Euclid's Algorithm?

Answer: For arbitrary numbers 702, 891, 621, 305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.