Highest Common Factor of 669, 902, 182 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 669, 902, 182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 902, 182 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 669, 902, 182 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 669, 902, 182 is 1.

HCF(669, 902, 182) = 1

HCF of 669, 902, 182 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 669, 902, 182 is 1.

Highest Common Factor of 669,902,182 using Euclid's algorithm

Highest Common Factor of 669,902,182 is 1

Step 1: Since 902 > 669, we apply the division lemma to 902 and 669, to get

902 = 669 x 1 + 233

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 233 and 669, to get

669 = 233 x 2 + 203

Step 3: We consider the new divisor 233 and the new remainder 203, and apply the division lemma to get

233 = 203 x 1 + 30

We consider the new divisor 203 and the new remainder 30,and apply the division lemma to get

203 = 30 x 6 + 23

We consider the new divisor 30 and the new remainder 23,and apply the division lemma to get

30 = 23 x 1 + 7

We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get

23 = 7 x 3 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 669 and 902 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(203,30) = HCF(233,203) = HCF(669,233) = HCF(902,669) .

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

Step 1: Since 182 > 1, we apply the division lemma to 182 and 1, to get

182 = 1 x 182 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 182 is 1

Notice that 1 = HCF(182,1) .

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Frequently Asked Questions on HCF of 669, 902, 182 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 669, 902, 182?

Answer: HCF of 669, 902, 182 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 902, 182 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 902, 182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.