Highest Common Factor of 2776, 8032, 53038 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 2776, 8032, 53038 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2776, 8032, 53038 is 2 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 2776, 8032, 53038 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 2776, 8032, 53038 is 2.
HCF(2776, 8032, 53038) = 2
HCF of 2776, 8032, 53038 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2776, 8032, 53038 is 2.
Highest Common Factor of 2776,8032,53038 is 2
Step 1: Since 8032 > 2776, we apply the division lemma to 8032 and 2776, to get
8032 = 2776 x 2 + 2480
Step 2: Since the reminder 2776 ≠ 0, we apply division lemma to 2480 and 2776, to get
2776 = 2480 x 1 + 296
Step 3: We consider the new divisor 2480 and the new remainder 296, and apply the division lemma to get
2480 = 296 x 8 + 112
We consider the new divisor 296 and the new remainder 112,and apply the division lemma to get
296 = 112 x 2 + 72
We consider the new divisor 112 and the new remainder 72,and apply the division lemma to get
112 = 72 x 1 + 40
We consider the new divisor 72 and the new remainder 40,and apply the division lemma to get
72 = 40 x 1 + 32
We consider the new divisor 40 and the new remainder 32,and apply the division lemma to get
40 = 32 x 1 + 8
We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get
32 = 8 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 2776 and 8032 is 8
Notice that 8 = HCF(32,8) = HCF(40,32) = HCF(72,40) = HCF(112,72) = HCF(296,112) = HCF(2480,296) = HCF(2776,2480) = HCF(8032,2776) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 53038 > 8, we apply the division lemma to 53038 and 8, to get
53038 = 8 x 6629 + 6
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 6 and 8, to get
8 = 6 x 1 + 2
Step 3: We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 53038 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(53038,8) .
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Frequently Asked Questions on HCF of 2776, 8032, 53038 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 2776, 8032, 53038?
Answer: HCF of 2776, 8032, 53038 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2776, 8032, 53038 using Euclid's Algorithm?
Answer: For arbitrary numbers 2776, 8032, 53038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.