Highest Common Factor of 270, 976, 522 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 270, 976, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 270, 976, 522 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 270, 976, 522 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 270, 976, 522 is 2.

HCF(270, 976, 522) = 2

HCF of 270, 976, 522 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 270, 976, 522 is 2.

Highest Common Factor of 270,976,522 using Euclid's algorithm

Highest Common Factor of 270,976,522 is 2

Step 1: Since 976 > 270, we apply the division lemma to 976 and 270, to get

976 = 270 x 3 + 166

Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 166 and 270, to get

270 = 166 x 1 + 104

Step 3: We consider the new divisor 166 and the new remainder 104, and apply the division lemma to get

166 = 104 x 1 + 62

We consider the new divisor 104 and the new remainder 62,and apply the division lemma to get

104 = 62 x 1 + 42

We consider the new divisor 62 and the new remainder 42,and apply the division lemma to get

62 = 42 x 1 + 20

We consider the new divisor 42 and the new remainder 20,and apply the division lemma to get

42 = 20 x 2 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 270 and 976 is 2

Notice that 2 = HCF(20,2) = HCF(42,20) = HCF(62,42) = HCF(104,62) = HCF(166,104) = HCF(270,166) = HCF(976,270) .

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

Step 1: Since 522 > 2, we apply the division lemma to 522 and 2, to get

522 = 2 x 261 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 522 is 2

Notice that 2 = HCF(522,2) .

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Frequently Asked Questions on HCF of 270, 976, 522 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 270, 976, 522?

Answer: HCF of 270, 976, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 270, 976, 522 using Euclid's Algorithm?

Answer: For arbitrary numbers 270, 976, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.