Highest Common Factor of 702, 590, 54 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, 590, 54 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 702, 590, 54 is 2 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, 590, 54 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, 590, 54 is 2.

HCF(702, 590, 54) = 2

HCF of 702, 590, 54 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, 590, 54 is 2.

Highest Common Factor of 702,590,54 using Euclid's algorithm

Highest Common Factor of 702,590,54 is 2

Step 1: Since 702 > 590, we apply the division lemma to 702 and 590, to get

702 = 590 x 1 + 112

Step 2: Since the reminder 590 ≠ 0, we apply division lemma to 112 and 590, to get

590 = 112 x 5 + 30

Step 3: We consider the new divisor 112 and the new remainder 30, and apply the division lemma to get

112 = 30 x 3 + 22

We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get

30 = 22 x 1 + 8

We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get

22 = 8 x 2 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 702 and 590 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(112,30) = HCF(590,112) = HCF(702,590) .

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

Step 1: Since 54 > 2, we apply the division lemma to 54 and 2, to get

54 = 2 x 27 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 54 is 2

Notice that 2 = HCF(54,2) .

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Frequently Asked Questions on HCF of 702, 590, 54 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, 590, 54?

Answer: HCF of 702, 590, 54 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 702, 590, 54 using Euclid's Algorithm?

Answer: For arbitrary numbers 702, 590, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.