Highest Common Factor of 1026, 8100, 50082 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 1026, 8100, 50082 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 1026, 8100, 50082 is 6 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 1026, 8100, 50082 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 1026, 8100, 50082 is 6.
HCF(1026, 8100, 50082) = 6
HCF of 1026, 8100, 50082 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1026, 8100, 50082 is 6.
Highest Common Factor of 1026,8100,50082 is 6
Step 1: Since 8100 > 1026, we apply the division lemma to 8100 and 1026, to get
8100 = 1026 x 7 + 918
Step 2: Since the reminder 1026 ≠ 0, we apply division lemma to 918 and 1026, to get
1026 = 918 x 1 + 108
Step 3: We consider the new divisor 918 and the new remainder 108, and apply the division lemma to get
918 = 108 x 8 + 54
We consider the new divisor 108 and the new remainder 54, and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 1026 and 8100 is 54
Notice that 54 = HCF(108,54) = HCF(918,108) = HCF(1026,918) = HCF(8100,1026) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 50082 > 54, we apply the division lemma to 50082 and 54, to get
50082 = 54 x 927 + 24
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 24 and 54, to get
54 = 24 x 2 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 54 and 50082 is 6
Notice that 6 = HCF(24,6) = HCF(54,24) = HCF(50082,54) .
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Frequently Asked Questions on HCF of 1026, 8100, 50082 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 1026, 8100, 50082?
Answer: HCF of 1026, 8100, 50082 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1026, 8100, 50082 using Euclid's Algorithm?
Answer: For arbitrary numbers 1026, 8100, 50082 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.