Highest Common Factor of 967, 720, 21 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 967, 720, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 967, 720, 21 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 967, 720, 21 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 967, 720, 21 is 1.

HCF(967, 720, 21) = 1

HCF of 967, 720, 21 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 967, 720, 21 is 1.

Highest Common Factor of 967,720,21 using Euclid's algorithm

Highest Common Factor of 967,720,21 is 1

Step 1: Since 967 > 720, we apply the division lemma to 967 and 720, to get

967 = 720 x 1 + 247

Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 247 and 720, to get

720 = 247 x 2 + 226

Step 3: We consider the new divisor 247 and the new remainder 226, and apply the division lemma to get

247 = 226 x 1 + 21

We consider the new divisor 226 and the new remainder 21,and apply the division lemma to get

226 = 21 x 10 + 16

We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get

21 = 16 x 1 + 5

We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get

16 = 5 x 3 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 720 is 1

Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(226,21) = HCF(247,226) = HCF(720,247) = HCF(967,720) .

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

Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get

21 = 1 x 21 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1

Notice that 1 = HCF(21,1) .

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Frequently Asked Questions on HCF of 967, 720, 21 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 967, 720, 21?

Answer: HCF of 967, 720, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 967, 720, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 967, 720, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.