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 434, 9709 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 434, 9709 is 7 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 434, 9709 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 434, 9709 is 7.
HCF(434, 9709) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 434, 9709 is 7.
Step 1: Since 9709 > 434, we apply the division lemma to 9709 and 434, to get
9709 = 434 x 22 + 161
Step 2: Since the reminder 434 ≠ 0, we apply division lemma to 161 and 434, to get
434 = 161 x 2 + 112
Step 3: We consider the new divisor 161 and the new remainder 112, and apply the division lemma to get
161 = 112 x 1 + 49
We consider the new divisor 112 and the new remainder 49,and apply the division lemma to get
112 = 49 x 2 + 14
We consider the new divisor 49 and the new remainder 14,and apply the division lemma to get
49 = 14 x 3 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 434 and 9709 is 7
Notice that 7 = HCF(14,7) = HCF(49,14) = HCF(112,49) = HCF(161,112) = HCF(434,161) = HCF(9709,434) .
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 434, 9709?
Answer: HCF of 434, 9709 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 434, 9709 using Euclid's Algorithm?
Answer: For arbitrary numbers 434, 9709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.