Highest Common Factor of 825, 522, 715 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 825, 522, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 522, 715 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 825, 522, 715 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 825, 522, 715 is 1.
HCF(825, 522, 715) = 1
HCF of 825, 522, 715 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 825, 522, 715 is 1.
Highest Common Factor of 825,522,715 is 1
Step 1: Since 825 > 522, we apply the division lemma to 825 and 522, to get
825 = 522 x 1 + 303
Step 2: Since the reminder 522 ≠ 0, we apply division lemma to 303 and 522, to get
522 = 303 x 1 + 219
Step 3: We consider the new divisor 303 and the new remainder 219, and apply the division lemma to get
303 = 219 x 1 + 84
We consider the new divisor 219 and the new remainder 84,and apply the division lemma to get
219 = 84 x 2 + 51
We consider the new divisor 84 and the new remainder 51,and apply the division lemma to get
84 = 51 x 1 + 33
We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 825 and 522 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(84,51) = HCF(219,84) = HCF(303,219) = HCF(522,303) = HCF(825,522) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 715 > 3, we apply the division lemma to 715 and 3, to get
715 = 3 x 238 + 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 715 is 1
Notice that 1 = HCF(3,1) = HCF(715,3) .
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Frequently Asked Questions on HCF of 825, 522, 715 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 825, 522, 715?
Answer: HCF of 825, 522, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 522, 715 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 522, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.