Highest Common Factor of 7217, 7574, 51765 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 7217, 7574, 51765 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 7217, 7574, 51765 is 7 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 7217, 7574, 51765 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 7217, 7574, 51765 is 7.
HCF(7217, 7574, 51765) = 7
HCF of 7217, 7574, 51765 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7217, 7574, 51765 is 7.
Highest Common Factor of 7217,7574,51765 is 7
Step 1: Since 7574 > 7217, we apply the division lemma to 7574 and 7217, to get
7574 = 7217 x 1 + 357
Step 2: Since the reminder 7217 ≠ 0, we apply division lemma to 357 and 7217, to get
7217 = 357 x 20 + 77
Step 3: We consider the new divisor 357 and the new remainder 77, and apply the division lemma to get
357 = 77 x 4 + 49
We consider the new divisor 77 and the new remainder 49,and apply the division lemma to get
77 = 49 x 1 + 28
We consider the new divisor 49 and the new remainder 28,and apply the division lemma to get
49 = 28 x 1 + 21
We consider the new divisor 28 and the new remainder 21,and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7217 and 7574 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(49,28) = HCF(77,49) = HCF(357,77) = HCF(7217,357) = HCF(7574,7217) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 51765 > 7, we apply the division lemma to 51765 and 7, to get
51765 = 7 x 7395 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 51765 is 7
Notice that 7 = HCF(51765,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 7217, 7574, 51765 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 7217, 7574, 51765?
Answer: HCF of 7217, 7574, 51765 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7217, 7574, 51765 using Euclid's Algorithm?
Answer: For arbitrary numbers 7217, 7574, 51765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.