Highest Common Factor of 9657, 2654, 32214 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 9657, 2654, 32214 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9657, 2654, 32214 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 9657, 2654, 32214 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 9657, 2654, 32214 is 1.

HCF(9657, 2654, 32214) = 1

HCF of 9657, 2654, 32214 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 9657, 2654, 32214 is 1.

Highest Common Factor of 9657,2654,32214 using Euclid's algorithm

Highest Common Factor of 9657,2654,32214 is 1

Step 1: Since 9657 > 2654, we apply the division lemma to 9657 and 2654, to get

9657 = 2654 x 3 + 1695

Step 2: Since the reminder 2654 ≠ 0, we apply division lemma to 1695 and 2654, to get

2654 = 1695 x 1 + 959

Step 3: We consider the new divisor 1695 and the new remainder 959, and apply the division lemma to get

1695 = 959 x 1 + 736

We consider the new divisor 959 and the new remainder 736,and apply the division lemma to get

959 = 736 x 1 + 223

We consider the new divisor 736 and the new remainder 223,and apply the division lemma to get

736 = 223 x 3 + 67

We consider the new divisor 223 and the new remainder 67,and apply the division lemma to get

223 = 67 x 3 + 22

We consider the new divisor 67 and the new remainder 22,and apply the division lemma to get

67 = 22 x 3 + 1

We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get

22 = 1 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9657 and 2654 is 1

Notice that 1 = HCF(22,1) = HCF(67,22) = HCF(223,67) = HCF(736,223) = HCF(959,736) = HCF(1695,959) = HCF(2654,1695) = HCF(9657,2654) .

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

Step 1: Since 32214 > 1, we apply the division lemma to 32214 and 1, to get

32214 = 1 x 32214 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32214 is 1

Notice that 1 = HCF(32214,1) .

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Frequently Asked Questions on HCF of 9657, 2654, 32214 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 9657, 2654, 32214?

Answer: HCF of 9657, 2654, 32214 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9657, 2654, 32214 using Euclid's Algorithm?

Answer: For arbitrary numbers 9657, 2654, 32214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.