Highest Common Factor of 748, 6679, 8508 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 748, 6679, 8508 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 6679, 8508 is 1 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 748, 6679, 8508 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 748, 6679, 8508 is 1.
HCF(748, 6679, 8508) = 1
HCF of 748, 6679, 8508 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 6679, 8508 is 1.
Highest Common Factor of 748,6679,8508 is 1
Step 1: Since 6679 > 748, we apply the division lemma to 6679 and 748, to get
6679 = 748 x 8 + 695
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 695 and 748, to get
748 = 695 x 1 + 53
Step 3: We consider the new divisor 695 and the new remainder 53, and apply the division lemma to get
695 = 53 x 13 + 6
We consider the new divisor 53 and the new remainder 6,and apply the division lemma to get
53 = 6 x 8 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 748 and 6679 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(53,6) = HCF(695,53) = HCF(748,695) = HCF(6679,748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8508 > 1, we apply the division lemma to 8508 and 1, to get
8508 = 1 x 8508 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8508 is 1
Notice that 1 = HCF(8508,1) .
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Frequently Asked Questions on HCF of 748, 6679, 8508 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 748, 6679, 8508?
Answer: HCF of 748, 6679, 8508 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 6679, 8508 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 6679, 8508 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
