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
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) 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) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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.