Highest Common Factor of 923, 670 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 923, 670 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 923, 670 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 923, 670 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 923, 670 is 1.

HCF(923, 670) = 1

HCF of 923, 670 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 923, 670 is 1.

Highest Common Factor of 923,670 using Euclid's algorithm

Highest Common Factor of 923,670 is 1

Step 1: Since 923 > 670, we apply the division lemma to 923 and 670, to get

923 = 670 x 1 + 253

Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 253 and 670, to get

670 = 253 x 2 + 164

Step 3: We consider the new divisor 253 and the new remainder 164, and apply the division lemma to get

253 = 164 x 1 + 89

We consider the new divisor 164 and the new remainder 89,and apply the division lemma to get

164 = 89 x 1 + 75

We consider the new divisor 89 and the new remainder 75,and apply the division lemma to get

89 = 75 x 1 + 14

We consider the new divisor 75 and the new remainder 14,and apply the division lemma to get

75 = 14 x 5 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 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 923 and 670 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(75,14) = HCF(89,75) = HCF(164,89) = HCF(253,164) = HCF(670,253) = HCF(923,670) .

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Frequently Asked Questions on HCF of 923, 670 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 923, 670?

Answer: HCF of 923, 670 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 923, 670 using Euclid's Algorithm?

Answer: For arbitrary numbers 923, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.