Highest Common Factor of 888, 7754 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 888, 7754 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 888, 7754 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 888, 7754 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 888, 7754 is 2.
HCF(888, 7754) = 2
HCF of 888, 7754 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 888, 7754 is 2.
Highest Common Factor of 888,7754 is 2
Step 1: Since 7754 > 888, we apply the division lemma to 7754 and 888, to get
7754 = 888 x 8 + 650
Step 2: Since the reminder 888 ≠ 0, we apply division lemma to 650 and 888, to get
888 = 650 x 1 + 238
Step 3: We consider the new divisor 650 and the new remainder 238, and apply the division lemma to get
650 = 238 x 2 + 174
We consider the new divisor 238 and the new remainder 174,and apply the division lemma to get
238 = 174 x 1 + 64
We consider the new divisor 174 and the new remainder 64,and apply the division lemma to get
174 = 64 x 2 + 46
We consider the new divisor 64 and the new remainder 46,and apply the division lemma to get
64 = 46 x 1 + 18
We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get
46 = 18 x 2 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 888 and 7754 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(64,46) = HCF(174,64) = HCF(238,174) = HCF(650,238) = HCF(888,650) = HCF(7754,888) .
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Frequently Asked Questions on HCF of 888, 7754 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 888, 7754?
Answer: HCF of 888, 7754 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 888, 7754 using Euclid's Algorithm?
Answer: For arbitrary numbers 888, 7754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.