Highest Common Factor of 552, 8038 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 552, 8038 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 552, 8038 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 552, 8038 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 552, 8038 is 2.
HCF(552, 8038) = 2
HCF of 552, 8038 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 552, 8038 is 2.
Highest Common Factor of 552,8038 is 2
Step 1: Since 8038 > 552, we apply the division lemma to 8038 and 552, to get
8038 = 552 x 14 + 310
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 310 and 552, to get
552 = 310 x 1 + 242
Step 3: We consider the new divisor 310 and the new remainder 242, and apply the division lemma to get
310 = 242 x 1 + 68
We consider the new divisor 242 and the new remainder 68,and apply the division lemma to get
242 = 68 x 3 + 38
We consider the new divisor 68 and the new remainder 38,and apply the division lemma to get
68 = 38 x 1 + 30
We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get
38 = 30 x 1 + 8
We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
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 552 and 8038 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(68,38) = HCF(242,68) = HCF(310,242) = HCF(552,310) = HCF(8038,552) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 552, 8038 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 552, 8038?
Answer: HCF of 552, 8038 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 552, 8038 using Euclid's Algorithm?
Answer: For arbitrary numbers 552, 8038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.