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 9704, 906 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9704, 906 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 9704, 906 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 9704, 906 is 2.
HCF(9704, 906) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9704, 906 is 2.
Step 1: Since 9704 > 906, we apply the division lemma to 9704 and 906, to get
9704 = 906 x 10 + 644
Step 2: Since the reminder 906 ≠ 0, we apply division lemma to 644 and 906, to get
906 = 644 x 1 + 262
Step 3: We consider the new divisor 644 and the new remainder 262, and apply the division lemma to get
644 = 262 x 2 + 120
We consider the new divisor 262 and the new remainder 120,and apply the division lemma to get
262 = 120 x 2 + 22
We consider the new divisor 120 and the new remainder 22,and apply the division lemma to get
120 = 22 x 5 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9704 and 906 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(120,22) = HCF(262,120) = HCF(644,262) = HCF(906,644) = HCF(9704,906) .
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 9704, 906?
Answer: HCF of 9704, 906 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9704, 906 using Euclid's Algorithm?
Answer: For arbitrary numbers 9704, 906 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.