Highest Common Factor of 975, 594, 276 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 975, 594, 276 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 594, 276 is 3 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 975, 594, 276 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 975, 594, 276 is 3.

HCF(975, 594, 276) = 3

HCF of 975, 594, 276 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 975, 594, 276 is 3.

Highest Common Factor of 975,594,276 using Euclid's algorithm

Highest Common Factor of 975,594,276 is 3

Step 1: Since 975 > 594, we apply the division lemma to 975 and 594, to get

975 = 594 x 1 + 381

Step 2: Since the reminder 594 ≠ 0, we apply division lemma to 381 and 594, to get

594 = 381 x 1 + 213

Step 3: We consider the new divisor 381 and the new remainder 213, and apply the division lemma to get

381 = 213 x 1 + 168

We consider the new divisor 213 and the new remainder 168,and apply the division lemma to get

213 = 168 x 1 + 45

We consider the new divisor 168 and the new remainder 45,and apply the division lemma to get

168 = 45 x 3 + 33

We consider the new divisor 45 and the new remainder 33,and apply the division lemma to get

45 = 33 x 1 + 12

We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get

33 = 12 x 2 + 9

We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get

12 = 9 x 1 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 975 and 594 is 3

Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(45,33) = HCF(168,45) = HCF(213,168) = HCF(381,213) = HCF(594,381) = HCF(975,594) .

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

Step 1: Since 276 > 3, we apply the division lemma to 276 and 3, to get

276 = 3 x 92 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 276 is 3

Notice that 3 = HCF(276,3) .

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Frequently Asked Questions on HCF of 975, 594, 276 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 975, 594, 276?

Answer: HCF of 975, 594, 276 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 594, 276 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 594, 276 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.