Highest Common Factor of 2964, 1971, 36245 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 2964, 1971, 36245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2964, 1971, 36245 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 2964, 1971, 36245 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 2964, 1971, 36245 is 1.

HCF(2964, 1971, 36245) = 1

HCF of 2964, 1971, 36245 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 2964, 1971, 36245 is 1.

Highest Common Factor of 2964,1971,36245 using Euclid's algorithm

Highest Common Factor of 2964,1971,36245 is 1

Step 1: Since 2964 > 1971, we apply the division lemma to 2964 and 1971, to get

2964 = 1971 x 1 + 993

Step 2: Since the reminder 1971 ≠ 0, we apply division lemma to 993 and 1971, to get

1971 = 993 x 1 + 978

Step 3: We consider the new divisor 993 and the new remainder 978, and apply the division lemma to get

993 = 978 x 1 + 15

We consider the new divisor 978 and the new remainder 15,and apply the division lemma to get

978 = 15 x 65 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2964 and 1971 is 3

Notice that 3 = HCF(15,3) = HCF(978,15) = HCF(993,978) = HCF(1971,993) = HCF(2964,1971) .

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

Step 1: Since 36245 > 3, we apply the division lemma to 36245 and 3, to get

36245 = 3 x 12081 + 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 36245 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(36245,3) .

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Frequently Asked Questions on HCF of 2964, 1971, 36245 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 2964, 1971, 36245?

Answer: HCF of 2964, 1971, 36245 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2964, 1971, 36245 using Euclid's Algorithm?

Answer: For arbitrary numbers 2964, 1971, 36245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.