Highest Common Factor of 97, 745, 66 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 97, 745, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 97, 745, 66 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 97, 745, 66 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 97, 745, 66 is 1.

HCF(97, 745, 66) = 1

HCF of 97, 745, 66 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 97, 745, 66 is 1.

Highest Common Factor of 97,745,66 using Euclid's algorithm

Highest Common Factor of 97,745,66 is 1

Step 1: Since 745 > 97, we apply the division lemma to 745 and 97, to get

745 = 97 x 7 + 66

Step 2: Since the reminder 97 ≠ 0, we apply division lemma to 66 and 97, to get

97 = 66 x 1 + 31

Step 3: We consider the new divisor 66 and the new remainder 31, and apply the division lemma to get

66 = 31 x 2 + 4

We consider the new divisor 31 and the new remainder 4,and apply the division lemma to get

31 = 4 x 7 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 97 and 745 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(31,4) = HCF(66,31) = HCF(97,66) = HCF(745,97) .

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

Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get

66 = 1 x 66 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1

Notice that 1 = HCF(66,1) .

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Frequently Asked Questions on HCF of 97, 745, 66 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 97, 745, 66?

Answer: HCF of 97, 745, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 97, 745, 66 using Euclid's Algorithm?

Answer: For arbitrary numbers 97, 745, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.