Highest Common Factor of 669, 714, 304 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, 714, 304 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 714, 304 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, 714, 304 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, 714, 304 is 1.

HCF(669, 714, 304) = 1

HCF of 669, 714, 304 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, 714, 304 is 1.

Highest Common Factor of 669,714,304 using Euclid's algorithm

Highest Common Factor of 669,714,304 is 1

Step 1: Since 714 > 669, we apply the division lemma to 714 and 669, to get

714 = 669 x 1 + 45

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 45 and 669, to get

669 = 45 x 14 + 39

Step 3: We consider the new divisor 45 and the new remainder 39, and apply the division lemma to get

45 = 39 x 1 + 6

We consider the new divisor 39 and the new remainder 6,and apply the division lemma to get

39 = 6 x 6 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 714 is 3

Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(45,39) = HCF(669,45) = HCF(714,669) .

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

Step 1: Since 304 > 3, we apply the division lemma to 304 and 3, to get

304 = 3 x 101 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 304 is 1

Notice that 1 = HCF(3,1) = HCF(304,3) .

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Frequently Asked Questions on HCF of 669, 714, 304 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, 714, 304?

Answer: HCF of 669, 714, 304 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 714, 304 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 714, 304 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.