Highest Common Factor of 9702, 742 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 9702, 742 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 9702, 742 is 14 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 9702, 742 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 9702, 742 is 14.
HCF(9702, 742) = 14
HCF of 9702, 742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9702, 742 is 14.
Highest Common Factor of 9702,742 is 14
Step 1: Since 9702 > 742, we apply the division lemma to 9702 and 742, to get
9702 = 742 x 13 + 56
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 56 and 742, to get
742 = 56 x 13 + 14
Step 3: We consider the new divisor 56 and the new remainder 14, and apply the division lemma to get
56 = 14 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 9702 and 742 is 14
Notice that 14 = HCF(56,14) = HCF(742,56) = HCF(9702,742) .
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Frequently Asked Questions on HCF of 9702, 742 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 9702, 742?
Answer: HCF of 9702, 742 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9702, 742 using Euclid's Algorithm?
Answer: For arbitrary numbers 9702, 742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.