Highest Common Factor of 414, 669, 653 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, 669, 653 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 414, 669, 653 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, 669, 653 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, 669, 653 is 1.

HCF(414, 669, 653) = 1

HCF of 414, 669, 653 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, 669, 653 is 1.

Highest Common Factor of 414,669,653 using Euclid's algorithm

Highest Common Factor of 414,669,653 is 1

Step 1: Since 669 > 414, we apply the division lemma to 669 and 414, to get

669 = 414 x 1 + 255

Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 255 and 414, to get

414 = 255 x 1 + 159

Step 3: We consider the new divisor 255 and the new remainder 159, and apply the division lemma to get

255 = 159 x 1 + 96

We consider the new divisor 159 and the new remainder 96,and apply the division lemma to get

159 = 96 x 1 + 63

We consider the new divisor 96 and the new remainder 63,and apply the division lemma to get

96 = 63 x 1 + 33

We consider the new divisor 63 and the new remainder 33,and apply the division lemma to get

63 = 33 x 1 + 30

We consider the new divisor 33 and the new remainder 30,and apply the division lemma to get

33 = 30 x 1 + 3

We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get

30 = 3 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 414 and 669 is 3

Notice that 3 = HCF(30,3) = HCF(33,30) = HCF(63,33) = HCF(96,63) = HCF(159,96) = HCF(255,159) = HCF(414,255) = HCF(669,414) .

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

Step 1: Since 653 > 3, we apply the division lemma to 653 and 3, to get

653 = 3 x 217 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 653 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(653,3) .

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Frequently Asked Questions on HCF of 414, 669, 653 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, 669, 653?

Answer: HCF of 414, 669, 653 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 414, 669, 653 using Euclid's Algorithm?

Answer: For arbitrary numbers 414, 669, 653 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.