Highest Common Factor of 77, 669, 177 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 77, 669, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 77, 669, 177 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 77, 669, 177 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 77, 669, 177 is 1.

HCF(77, 669, 177) = 1

HCF of 77, 669, 177 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 77, 669, 177 is 1.

Highest Common Factor of 77,669,177 using Euclid's algorithm

Highest Common Factor of 77,669,177 is 1

Step 1: Since 669 > 77, we apply the division lemma to 669 and 77, to get

669 = 77 x 8 + 53

Step 2: Since the reminder 77 ≠ 0, we apply division lemma to 53 and 77, to get

77 = 53 x 1 + 24

Step 3: We consider the new divisor 53 and the new remainder 24, and apply the division lemma to get

53 = 24 x 2 + 5

We consider the new divisor 24 and the new remainder 5,and apply the division lemma to get

24 = 5 x 4 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 77 and 669 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(24,5) = HCF(53,24) = HCF(77,53) = HCF(669,77) .

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

Step 1: Since 177 > 1, we apply the division lemma to 177 and 1, to get

177 = 1 x 177 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 177 is 1

Notice that 1 = HCF(177,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 77, 669, 177 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 77, 669, 177?

Answer: HCF of 77, 669, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 77, 669, 177 using Euclid's Algorithm?

Answer: For arbitrary numbers 77, 669, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.