Highest Common Factor of 172, 276, 690 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 172, 276, 690 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 172, 276, 690 is 2 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 172, 276, 690 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 172, 276, 690 is 2.

HCF(172, 276, 690) = 2

HCF of 172, 276, 690 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 172, 276, 690 is 2.

Highest Common Factor of 172,276,690 using Euclid's algorithm

Highest Common Factor of 172,276,690 is 2

Step 1: Since 276 > 172, we apply the division lemma to 276 and 172, to get

276 = 172 x 1 + 104

Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 104 and 172, to get

172 = 104 x 1 + 68

Step 3: We consider the new divisor 104 and the new remainder 68, and apply the division lemma to get

104 = 68 x 1 + 36

We consider the new divisor 68 and the new remainder 36,and apply the division lemma to get

68 = 36 x 1 + 32

We consider the new divisor 36 and the new remainder 32,and apply the division lemma to get

36 = 32 x 1 + 4

We consider the new divisor 32 and the new remainder 4,and apply the division lemma to get

32 = 4 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 172 and 276 is 4

Notice that 4 = HCF(32,4) = HCF(36,32) = HCF(68,36) = HCF(104,68) = HCF(172,104) = HCF(276,172) .

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

Step 1: Since 690 > 4, we apply the division lemma to 690 and 4, to get

690 = 4 x 172 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 690 is 2

Notice that 2 = HCF(4,2) = HCF(690,4) .

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Frequently Asked Questions on HCF of 172, 276, 690 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 172, 276, 690?

Answer: HCF of 172, 276, 690 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 172, 276, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 172, 276, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.