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 8106, 9574 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8106, 9574 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 8106, 9574 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 8106, 9574 is 2.
HCF(8106, 9574) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8106, 9574 is 2.
Step 1: Since 9574 > 8106, we apply the division lemma to 9574 and 8106, to get
9574 = 8106 x 1 + 1468
Step 2: Since the reminder 8106 ≠ 0, we apply division lemma to 1468 and 8106, to get
8106 = 1468 x 5 + 766
Step 3: We consider the new divisor 1468 and the new remainder 766, and apply the division lemma to get
1468 = 766 x 1 + 702
We consider the new divisor 766 and the new remainder 702,and apply the division lemma to get
766 = 702 x 1 + 64
We consider the new divisor 702 and the new remainder 64,and apply the division lemma to get
702 = 64 x 10 + 62
We consider the new divisor 64 and the new remainder 62,and apply the division lemma to get
64 = 62 x 1 + 2
We consider the new divisor 62 and the new remainder 2,and apply the division lemma to get
62 = 2 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8106 and 9574 is 2
Notice that 2 = HCF(62,2) = HCF(64,62) = HCF(702,64) = HCF(766,702) = HCF(1468,766) = HCF(8106,1468) = HCF(9574,8106) .
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 8106, 9574?
Answer: HCF of 8106, 9574 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8106, 9574 using Euclid's Algorithm?
Answer: For arbitrary numbers 8106, 9574 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.