Highest Common Factor of 690, 504, 884 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 690, 504, 884 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 504, 884 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 690, 504, 884 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 690, 504, 884 is 2.

HCF(690, 504, 884) = 2

HCF of 690, 504, 884 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 690, 504, 884 is 2.

Highest Common Factor of 690,504,884 using Euclid's algorithm

Highest Common Factor of 690,504,884 is 2

Step 1: Since 690 > 504, we apply the division lemma to 690 and 504, to get

690 = 504 x 1 + 186

Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 186 and 504, to get

504 = 186 x 2 + 132

Step 3: We consider the new divisor 186 and the new remainder 132, and apply the division lemma to get

186 = 132 x 1 + 54

We consider the new divisor 132 and the new remainder 54,and apply the division lemma to get

132 = 54 x 2 + 24

We consider the new divisor 54 and the new remainder 24,and apply the division lemma to get

54 = 24 x 2 + 6

We consider the new divisor 24 and the new remainder 6,and apply the division lemma to get

24 = 6 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 690 and 504 is 6

Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(132,54) = HCF(186,132) = HCF(504,186) = HCF(690,504) .

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

Step 1: Since 884 > 6, we apply the division lemma to 884 and 6, to get

884 = 6 x 147 + 2

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 884 is 2

Notice that 2 = HCF(6,2) = HCF(884,6) .

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Frequently Asked Questions on HCF of 690, 504, 884 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 690, 504, 884?

Answer: HCF of 690, 504, 884 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 504, 884 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 504, 884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.