Highest Common Factor of 353, 964, 770, 669 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 353, 964, 770, 669 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 353, 964, 770, 669 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 353, 964, 770, 669 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 353, 964, 770, 669 is 1.

HCF(353, 964, 770, 669) = 1

HCF of 353, 964, 770, 669 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 353, 964, 770, 669 is 1.

Highest Common Factor of 353,964,770,669 using Euclid's algorithm

Highest Common Factor of 353,964,770,669 is 1

Step 1: Since 964 > 353, we apply the division lemma to 964 and 353, to get

964 = 353 x 2 + 258

Step 2: Since the reminder 353 ≠ 0, we apply division lemma to 258 and 353, to get

353 = 258 x 1 + 95

Step 3: We consider the new divisor 258 and the new remainder 95, and apply the division lemma to get

258 = 95 x 2 + 68

We consider the new divisor 95 and the new remainder 68,and apply the division lemma to get

95 = 68 x 1 + 27

We consider the new divisor 68 and the new remainder 27,and apply the division lemma to get

68 = 27 x 2 + 14

We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get

27 = 14 x 1 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 353 and 964 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(68,27) = HCF(95,68) = HCF(258,95) = HCF(353,258) = HCF(964,353) .

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

Step 1: Since 770 > 1, we apply the division lemma to 770 and 1, to get

770 = 1 x 770 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 770 is 1

Notice that 1 = HCF(770,1) .

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

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

669 = 1 x 669 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 669 is 1

Notice that 1 = HCF(669,1) .

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Frequently Asked Questions on HCF of 353, 964, 770, 669 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 353, 964, 770, 669?

Answer: HCF of 353, 964, 770, 669 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 353, 964, 770, 669 using Euclid's Algorithm?

Answer: For arbitrary numbers 353, 964, 770, 669 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.