Highest Common Factor of 448, 3926, 8665 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 448, 3926, 8665 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 3926, 8665 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 448, 3926, 8665 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 448, 3926, 8665 is 1.
HCF(448, 3926, 8665) = 1
HCF of 448, 3926, 8665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 3926, 8665 is 1.
Highest Common Factor of 448,3926,8665 is 1
Step 1: Since 3926 > 448, we apply the division lemma to 3926 and 448, to get
3926 = 448 x 8 + 342
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 342 and 448, to get
448 = 342 x 1 + 106
Step 3: We consider the new divisor 342 and the new remainder 106, and apply the division lemma to get
342 = 106 x 3 + 24
We consider the new divisor 106 and the new remainder 24,and apply the division lemma to get
106 = 24 x 4 + 10
We consider the new divisor 24 and the new remainder 10,and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 448 and 3926 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(106,24) = HCF(342,106) = HCF(448,342) = HCF(3926,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8665 > 2, we apply the division lemma to 8665 and 2, to get
8665 = 2 x 4332 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 8665 is 1
Notice that 1 = HCF(2,1) = HCF(8665,2) .
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Frequently Asked Questions on HCF of 448, 3926, 8665 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 448, 3926, 8665?
Answer: HCF of 448, 3926, 8665 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 3926, 8665 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 3926, 8665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.