Highest Common Factor of 5016, 2664, 61920 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 5016, 2664, 61920 i.e. 24 the largest integer that leaves a remainder zero for all numbers.

HCF of 5016, 2664, 61920 is 24 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 5016, 2664, 61920 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 5016, 2664, 61920 is 24.

HCF(5016, 2664, 61920) = 24

HCF of 5016, 2664, 61920 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 5016, 2664, 61920 is 24.

Highest Common Factor of 5016,2664,61920 using Euclid's algorithm

Highest Common Factor of 5016,2664,61920 is 24

Step 1: Since 5016 > 2664, we apply the division lemma to 5016 and 2664, to get

5016 = 2664 x 1 + 2352

Step 2: Since the reminder 2664 ≠ 0, we apply division lemma to 2352 and 2664, to get

2664 = 2352 x 1 + 312

Step 3: We consider the new divisor 2352 and the new remainder 312, and apply the division lemma to get

2352 = 312 x 7 + 168

We consider the new divisor 312 and the new remainder 168,and apply the division lemma to get

312 = 168 x 1 + 144

We consider the new divisor 168 and the new remainder 144,and apply the division lemma to get

168 = 144 x 1 + 24

We consider the new divisor 144 and the new remainder 24,and apply the division lemma to get

144 = 24 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 5016 and 2664 is 24

Notice that 24 = HCF(144,24) = HCF(168,144) = HCF(312,168) = HCF(2352,312) = HCF(2664,2352) = HCF(5016,2664) .

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

Step 1: Since 61920 > 24, we apply the division lemma to 61920 and 24, to get

61920 = 24 x 2580 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 24 and 61920 is 24

Notice that 24 = HCF(61920,24) .

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Frequently Asked Questions on HCF of 5016, 2664, 61920 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 5016, 2664, 61920?

Answer: HCF of 5016, 2664, 61920 is 24 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5016, 2664, 61920 using Euclid's Algorithm?

Answer: For arbitrary numbers 5016, 2664, 61920 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.