Highest Common Factor of 673, 160, 36 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 673, 160, 36 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 673, 160, 36 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 673, 160, 36 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 673, 160, 36 is 1.

HCF(673, 160, 36) = 1

HCF of 673, 160, 36 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 673, 160, 36 is 1.

Highest Common Factor of 673,160,36 using Euclid's algorithm

Highest Common Factor of 673,160,36 is 1

Step 1: Since 673 > 160, we apply the division lemma to 673 and 160, to get

673 = 160 x 4 + 33

Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 33 and 160, to get

160 = 33 x 4 + 28

Step 3: We consider the new divisor 33 and the new remainder 28, and apply the division lemma to get

33 = 28 x 1 + 5

We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get

28 = 5 x 5 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 673 and 160 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(33,28) = HCF(160,33) = HCF(673,160) .

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

Step 1: Since 36 > 1, we apply the division lemma to 36 and 1, to get

36 = 1 x 36 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 36 is 1

Notice that 1 = HCF(36,1) .

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Frequently Asked Questions on HCF of 673, 160, 36 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 673, 160, 36?

Answer: HCF of 673, 160, 36 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 673, 160, 36 using Euclid's Algorithm?

Answer: For arbitrary numbers 673, 160, 36 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.