Highest Common Factor of 5001, 8574, 77314 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 5001, 8574, 77314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5001, 8574, 77314 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 5001, 8574, 77314 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 5001, 8574, 77314 is 1.
HCF(5001, 8574, 77314) = 1
HCF of 5001, 8574, 77314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5001, 8574, 77314 is 1.
Highest Common Factor of 5001,8574,77314 is 1
Step 1: Since 8574 > 5001, we apply the division lemma to 8574 and 5001, to get
8574 = 5001 x 1 + 3573
Step 2: Since the reminder 5001 ≠ 0, we apply division lemma to 3573 and 5001, to get
5001 = 3573 x 1 + 1428
Step 3: We consider the new divisor 3573 and the new remainder 1428, and apply the division lemma to get
3573 = 1428 x 2 + 717
We consider the new divisor 1428 and the new remainder 717,and apply the division lemma to get
1428 = 717 x 1 + 711
We consider the new divisor 717 and the new remainder 711,and apply the division lemma to get
717 = 711 x 1 + 6
We consider the new divisor 711 and the new remainder 6,and apply the division lemma to get
711 = 6 x 118 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 5001 and 8574 is 3
Notice that 3 = HCF(6,3) = HCF(711,6) = HCF(717,711) = HCF(1428,717) = HCF(3573,1428) = HCF(5001,3573) = HCF(8574,5001) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77314 > 3, we apply the division lemma to 77314 and 3, to get
77314 = 3 x 25771 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 77314 is 1
Notice that 1 = HCF(3,1) = HCF(77314,3) .
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Frequently Asked Questions on HCF of 5001, 8574, 77314 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 5001, 8574, 77314?
Answer: HCF of 5001, 8574, 77314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5001, 8574, 77314 using Euclid's Algorithm?
Answer: For arbitrary numbers 5001, 8574, 77314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
