Highest Common Factor of 414, 668, 309 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 414, 668, 309 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 414, 668, 309 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 414, 668, 309 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 414, 668, 309 is 1.

HCF(414, 668, 309) = 1

HCF of 414, 668, 309 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 414, 668, 309 is 1.

Highest Common Factor of 414,668,309 using Euclid's algorithm

Highest Common Factor of 414,668,309 is 1

Step 1: Since 668 > 414, we apply the division lemma to 668 and 414, to get

668 = 414 x 1 + 254

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 254 and 414, to get

414 = 254 x 1 + 160

Step 3: We consider the new divisor 254 and the new remainder 160, and apply the division lemma to get

254 = 160 x 1 + 94

We consider the new divisor 160 and the new remainder 94,and apply the division lemma to get

160 = 94 x 1 + 66

We consider the new divisor 94 and the new remainder 66,and apply the division lemma to get

94 = 66 x 1 + 28

We consider the new divisor 66 and the new remainder 28,and apply the division lemma to get

66 = 28 x 2 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 414 and 668 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(66,28) = HCF(94,66) = HCF(160,94) = HCF(254,160) = HCF(414,254) = HCF(668,414) .

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

Step 1: Since 309 > 2, we apply the division lemma to 309 and 2, to get

309 = 2 x 154 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 309 is 1

Notice that 1 = HCF(2,1) = HCF(309,2) .

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Frequently Asked Questions on HCF of 414, 668, 309 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 414, 668, 309?

Answer: HCF of 414, 668, 309 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 414, 668, 309 using Euclid's Algorithm?

Answer: For arbitrary numbers 414, 668, 309 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.