Highest Common Factor of 6888, 7542, 85828 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 6888, 7542, 85828 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6888, 7542, 85828 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 6888, 7542, 85828 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 6888, 7542, 85828 is 2.
HCF(6888, 7542, 85828) = 2
HCF of 6888, 7542, 85828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6888, 7542, 85828 is 2.
Highest Common Factor of 6888,7542,85828 is 2
Step 1: Since 7542 > 6888, we apply the division lemma to 7542 and 6888, to get
7542 = 6888 x 1 + 654
Step 2: Since the reminder 6888 ≠ 0, we apply division lemma to 654 and 6888, to get
6888 = 654 x 10 + 348
Step 3: We consider the new divisor 654 and the new remainder 348, and apply the division lemma to get
654 = 348 x 1 + 306
We consider the new divisor 348 and the new remainder 306,and apply the division lemma to get
348 = 306 x 1 + 42
We consider the new divisor 306 and the new remainder 42,and apply the division lemma to get
306 = 42 x 7 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6888 and 7542 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(306,42) = HCF(348,306) = HCF(654,348) = HCF(6888,654) = HCF(7542,6888) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85828 > 6, we apply the division lemma to 85828 and 6, to get
85828 = 6 x 14304 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 85828 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(85828,6) .
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Frequently Asked Questions on HCF of 6888, 7542, 85828 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 6888, 7542, 85828?
Answer: HCF of 6888, 7542, 85828 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6888, 7542, 85828 using Euclid's Algorithm?
Answer: For arbitrary numbers 6888, 7542, 85828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.