Highest Common Factor of 496, 673, 138 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 496, 673, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 496, 673, 138 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 496, 673, 138 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 496, 673, 138 is 1.

HCF(496, 673, 138) = 1

HCF of 496, 673, 138 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 496, 673, 138 is 1.

Highest Common Factor of 496,673,138 using Euclid's algorithm

Highest Common Factor of 496,673,138 is 1

Step 1: Since 673 > 496, we apply the division lemma to 673 and 496, to get

673 = 496 x 1 + 177

Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 177 and 496, to get

496 = 177 x 2 + 142

Step 3: We consider the new divisor 177 and the new remainder 142, and apply the division lemma to get

177 = 142 x 1 + 35

We consider the new divisor 142 and the new remainder 35,and apply the division lemma to get

142 = 35 x 4 + 2

We consider the new divisor 35 and the new remainder 2,and apply the division lemma to get

35 = 2 x 17 + 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 496 and 673 is 1

Notice that 1 = HCF(2,1) = HCF(35,2) = HCF(142,35) = HCF(177,142) = HCF(496,177) = HCF(673,496) .

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

Step 1: Since 138 > 1, we apply the division lemma to 138 and 1, to get

138 = 1 x 138 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 138 is 1

Notice that 1 = HCF(138,1) .

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Frequently Asked Questions on HCF of 496, 673, 138 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 496, 673, 138?

Answer: HCF of 496, 673, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 496, 673, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 496, 673, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.