Highest Common Factor of 854, 10748 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 854, 10748 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 854, 10748 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 854, 10748 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 854, 10748 is 2.
HCF(854, 10748) = 2
HCF of 854, 10748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 854, 10748 is 2.
Highest Common Factor of 854,10748 is 2
Step 1: Since 10748 > 854, we apply the division lemma to 10748 and 854, to get
10748 = 854 x 12 + 500
Step 2: Since the reminder 854 ≠ 0, we apply division lemma to 500 and 854, to get
854 = 500 x 1 + 354
Step 3: We consider the new divisor 500 and the new remainder 354, and apply the division lemma to get
500 = 354 x 1 + 146
We consider the new divisor 354 and the new remainder 146,and apply the division lemma to get
354 = 146 x 2 + 62
We consider the new divisor 146 and the new remainder 62,and apply the division lemma to get
146 = 62 x 2 + 22
We consider the new divisor 62 and the new remainder 22,and apply the division lemma to get
62 = 22 x 2 + 18
We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get
22 = 18 x 1 + 4
We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get
18 = 4 x 4 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 854 and 10748 is 2
Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(62,22) = HCF(146,62) = HCF(354,146) = HCF(500,354) = HCF(854,500) = HCF(10748,854) .
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Frequently Asked Questions on HCF of 854, 10748 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 854, 10748?
Answer: HCF of 854, 10748 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 854, 10748 using Euclid's Algorithm?
Answer: For arbitrary numbers 854, 10748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.