Highest Common Factor of 657, 967, 407, 23 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 657, 967, 407, 23 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 967, 407, 23 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 657, 967, 407, 23 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 657, 967, 407, 23 is 1.

HCF(657, 967, 407, 23) = 1

HCF of 657, 967, 407, 23 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 657, 967, 407, 23 is 1.

Highest Common Factor of 657,967,407,23 using Euclid's algorithm

Highest Common Factor of 657,967,407,23 is 1

Step 1: Since 967 > 657, we apply the division lemma to 967 and 657, to get

967 = 657 x 1 + 310

Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 310 and 657, to get

657 = 310 x 2 + 37

Step 3: We consider the new divisor 310 and the new remainder 37, and apply the division lemma to get

310 = 37 x 8 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 657 and 967 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(310,37) = HCF(657,310) = HCF(967,657) .

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

Step 1: Since 407 > 1, we apply the division lemma to 407 and 1, to get

407 = 1 x 407 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 407 is 1

Notice that 1 = HCF(407,1) .

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

Step 1: Since 23 > 1, we apply the division lemma to 23 and 1, to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 23 is 1

Notice that 1 = HCF(23,1) .

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Frequently Asked Questions on HCF of 657, 967, 407, 23 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 657, 967, 407, 23?

Answer: HCF of 657, 967, 407, 23 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 967, 407, 23 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 967, 407, 23 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.