Highest Common Factor of 807, 487, 654, 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 807, 487, 654, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 807, 487, 654, 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 807, 487, 654, 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 807, 487, 654, 21 is 1.

HCF(807, 487, 654, 21) = 1

HCF of 807, 487, 654, 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 807, 487, 654, 21 is 1.

Highest Common Factor of 807,487,654,21 using Euclid's algorithm

Highest Common Factor of 807,487,654,21 is 1

Step 1: Since 807 > 487, we apply the division lemma to 807 and 487, to get

807 = 487 x 1 + 320

Step 2: Since the reminder 487 ≠ 0, we apply division lemma to 320 and 487, to get

487 = 320 x 1 + 167

Step 3: We consider the new divisor 320 and the new remainder 167, and apply the division lemma to get

320 = 167 x 1 + 153

We consider the new divisor 167 and the new remainder 153,and apply the division lemma to get

167 = 153 x 1 + 14

We consider the new divisor 153 and the new remainder 14,and apply the division lemma to get

153 = 14 x 10 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 807 and 487 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(153,14) = HCF(167,153) = HCF(320,167) = HCF(487,320) = HCF(807,487) .

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

Step 1: Since 654 > 1, we apply the division lemma to 654 and 1, to get

654 = 1 x 654 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 654 is 1

Notice that 1 = HCF(654,1) .

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 807, 487, 654, 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 807, 487, 654, 21?

Answer: HCF of 807, 487, 654, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 807, 487, 654, 21 using Euclid's Algorithm?

Answer: For arbitrary numbers 807, 487, 654, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.