Highest Common Factor of 828, 659, 421 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 828, 659, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 828, 659, 421 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 828, 659, 421 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 828, 659, 421 is 1.

HCF(828, 659, 421) = 1

HCF of 828, 659, 421 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 828, 659, 421 is 1.

Highest Common Factor of 828,659,421 using Euclid's algorithm

Highest Common Factor of 828,659,421 is 1

Step 1: Since 828 > 659, we apply the division lemma to 828 and 659, to get

828 = 659 x 1 + 169

Step 2: Since the reminder 659 ≠ 0, we apply division lemma to 169 and 659, to get

659 = 169 x 3 + 152

Step 3: We consider the new divisor 169 and the new remainder 152, and apply the division lemma to get

169 = 152 x 1 + 17

We consider the new divisor 152 and the new remainder 17,and apply the division lemma to get

152 = 17 x 8 + 16

We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get

17 = 16 x 1 + 1

We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 828 and 659 is 1

Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(152,17) = HCF(169,152) = HCF(659,169) = HCF(828,659) .

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

Step 1: Since 421 > 1, we apply the division lemma to 421 and 1, to get

421 = 1 x 421 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 421 is 1

Notice that 1 = HCF(421,1) .

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Frequently Asked Questions on HCF of 828, 659, 421 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 828, 659, 421?

Answer: HCF of 828, 659, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 828, 659, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 828, 659, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.