Highest Common Factor of 896, 6742 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 896, 6742 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 896, 6742 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 896, 6742 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 896, 6742 is 2.
HCF(896, 6742) = 2
HCF of 896, 6742 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 896, 6742 is 2.
Highest Common Factor of 896,6742 is 2
Step 1: Since 6742 > 896, we apply the division lemma to 6742 and 896, to get
6742 = 896 x 7 + 470
Step 2: Since the reminder 896 ≠ 0, we apply division lemma to 470 and 896, to get
896 = 470 x 1 + 426
Step 3: We consider the new divisor 470 and the new remainder 426, and apply the division lemma to get
470 = 426 x 1 + 44
We consider the new divisor 426 and the new remainder 44,and apply the division lemma to get
426 = 44 x 9 + 30
We consider the new divisor 44 and the new remainder 30,and apply the division lemma to get
44 = 30 x 1 + 14
We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get
30 = 14 x 2 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 896 and 6742 is 2
Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(44,30) = HCF(426,44) = HCF(470,426) = HCF(896,470) = HCF(6742,896) .
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Frequently Asked Questions on HCF of 896, 6742 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 896, 6742?
Answer: HCF of 896, 6742 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 896, 6742 using Euclid's Algorithm?
Answer: For arbitrary numbers 896, 6742 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
