Highest Common Factor of 753, 292, 166 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 753, 292, 166 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 753, 292, 166 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 753, 292, 166 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 753, 292, 166 is 1.

HCF(753, 292, 166) = 1

HCF of 753, 292, 166 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 753, 292, 166 is 1.

Highest Common Factor of 753,292,166 using Euclid's algorithm

Highest Common Factor of 753,292,166 is 1

Step 1: Since 753 > 292, we apply the division lemma to 753 and 292, to get

753 = 292 x 2 + 169

Step 2: Since the reminder 292 ≠ 0, we apply division lemma to 169 and 292, to get

292 = 169 x 1 + 123

Step 3: We consider the new divisor 169 and the new remainder 123, and apply the division lemma to get

169 = 123 x 1 + 46

We consider the new divisor 123 and the new remainder 46,and apply the division lemma to get

123 = 46 x 2 + 31

We consider the new divisor 46 and the new remainder 31,and apply the division lemma to get

46 = 31 x 1 + 15

We consider the new divisor 31 and the new remainder 15,and apply the division lemma to get

31 = 15 x 2 + 1

We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get

15 = 1 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 753 and 292 is 1

Notice that 1 = HCF(15,1) = HCF(31,15) = HCF(46,31) = HCF(123,46) = HCF(169,123) = HCF(292,169) = HCF(753,292) .

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

Step 1: Since 166 > 1, we apply the division lemma to 166 and 1, to get

166 = 1 x 166 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 166 is 1

Notice that 1 = HCF(166,1) .

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Frequently Asked Questions on HCF of 753, 292, 166 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 753, 292, 166?

Answer: HCF of 753, 292, 166 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 753, 292, 166 using Euclid's Algorithm?

Answer: For arbitrary numbers 753, 292, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.