Highest Common Factor of 279, 735, 967 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 279, 735, 967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 279, 735, 967 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 279, 735, 967 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 279, 735, 967 is 1.

HCF(279, 735, 967) = 1

HCF of 279, 735, 967 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 279, 735, 967 is 1.

Highest Common Factor of 279,735,967 using Euclid's algorithm

Highest Common Factor of 279,735,967 is 1

Step 1: Since 735 > 279, we apply the division lemma to 735 and 279, to get

735 = 279 x 2 + 177

Step 2: Since the reminder 279 ≠ 0, we apply division lemma to 177 and 279, to get

279 = 177 x 1 + 102

Step 3: We consider the new divisor 177 and the new remainder 102, and apply the division lemma to get

177 = 102 x 1 + 75

We consider the new divisor 102 and the new remainder 75,and apply the division lemma to get

102 = 75 x 1 + 27

We consider the new divisor 75 and the new remainder 27,and apply the division lemma to get

75 = 27 x 2 + 21

We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get

27 = 21 x 1 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 279 and 735 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(75,27) = HCF(102,75) = HCF(177,102) = HCF(279,177) = HCF(735,279) .

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

Step 1: Since 967 > 3, we apply the division lemma to 967 and 3, to get

967 = 3 x 322 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 967 is 1

Notice that 1 = HCF(3,1) = HCF(967,3) .

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Frequently Asked Questions on HCF of 279, 735, 967 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 279, 735, 967?

Answer: HCF of 279, 735, 967 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 279, 735, 967 using Euclid's Algorithm?

Answer: For arbitrary numbers 279, 735, 967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.