Highest Common Factor of 774, 167, 209, 232 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 774, 167, 209, 232 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 774, 167, 209, 232 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 774, 167, 209, 232 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 774, 167, 209, 232 is 1.

HCF(774, 167, 209, 232) = 1

HCF of 774, 167, 209, 232 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 774, 167, 209, 232 is 1.

Highest Common Factor of 774,167,209,232 using Euclid's algorithm

Highest Common Factor of 774,167,209,232 is 1

Step 1: Since 774 > 167, we apply the division lemma to 774 and 167, to get

774 = 167 x 4 + 106

Step 2: Since the reminder 167 ≠ 0, we apply division lemma to 106 and 167, to get

167 = 106 x 1 + 61

Step 3: We consider the new divisor 106 and the new remainder 61, and apply the division lemma to get

106 = 61 x 1 + 45

We consider the new divisor 61 and the new remainder 45,and apply the division lemma to get

61 = 45 x 1 + 16

We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get

45 = 16 x 2 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 774 and 167 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(61,45) = HCF(106,61) = HCF(167,106) = HCF(774,167) .

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

Step 1: Since 209 > 1, we apply the division lemma to 209 and 1, to get

209 = 1 x 209 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 209 is 1

Notice that 1 = HCF(209,1) .

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

Step 1: Since 232 > 1, we apply the division lemma to 232 and 1, to get

232 = 1 x 232 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 232 is 1

Notice that 1 = HCF(232,1) .

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Frequently Asked Questions on HCF of 774, 167, 209, 232 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 774, 167, 209, 232?

Answer: HCF of 774, 167, 209, 232 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 774, 167, 209, 232 using Euclid's Algorithm?

Answer: For arbitrary numbers 774, 167, 209, 232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.