Highest Common Factor of 336, 891, 35 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 336, 891, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 336, 891, 35 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 336, 891, 35 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 336, 891, 35 is 1.

HCF(336, 891, 35) = 1

HCF of 336, 891, 35 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 336, 891, 35 is 1.

Highest Common Factor of 336,891,35 using Euclid's algorithm

Highest Common Factor of 336,891,35 is 1

Step 1: Since 891 > 336, we apply the division lemma to 891 and 336, to get

891 = 336 x 2 + 219

Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 219 and 336, to get

336 = 219 x 1 + 117

Step 3: We consider the new divisor 219 and the new remainder 117, and apply the division lemma to get

219 = 117 x 1 + 102

We consider the new divisor 117 and the new remainder 102,and apply the division lemma to get

117 = 102 x 1 + 15

We consider the new divisor 102 and the new remainder 15,and apply the division lemma to get

102 = 15 x 6 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 336 and 891 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(102,15) = HCF(117,102) = HCF(219,117) = HCF(336,219) = HCF(891,336) .

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

Step 1: Since 35 > 3, we apply the division lemma to 35 and 3, to get

35 = 3 x 11 + 2

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

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 35 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(35,3) .

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Frequently Asked Questions on HCF of 336, 891, 35 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 336, 891, 35?

Answer: HCF of 336, 891, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 336, 891, 35 using Euclid's Algorithm?

Answer: For arbitrary numbers 336, 891, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.