Highest Common Factor of 512, 825, 124 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 512, 825, 124 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 825, 124 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 512, 825, 124 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 512, 825, 124 is 1.
HCF(512, 825, 124) = 1
HCF of 512, 825, 124 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 825, 124 is 1.
Highest Common Factor of 512,825,124 is 1
Step 1: Since 825 > 512, we apply the division lemma to 825 and 512, to get
825 = 512 x 1 + 313
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 313 and 512, to get
512 = 313 x 1 + 199
Step 3: We consider the new divisor 313 and the new remainder 199, and apply the division lemma to get
313 = 199 x 1 + 114
We consider the new divisor 199 and the new remainder 114,and apply the division lemma to get
199 = 114 x 1 + 85
We consider the new divisor 114 and the new remainder 85,and apply the division lemma to get
114 = 85 x 1 + 29
We consider the new divisor 85 and the new remainder 29,and apply the division lemma to get
85 = 29 x 2 + 27
We consider the new divisor 29 and the new remainder 27,and apply the division lemma to get
29 = 27 x 1 + 2
We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get
27 = 2 x 13 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 512 and 825 is 1
Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(29,27) = HCF(85,29) = HCF(114,85) = HCF(199,114) = HCF(313,199) = HCF(512,313) = HCF(825,512) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 124 > 1, we apply the division lemma to 124 and 1, to get
124 = 1 x 124 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 124 is 1
Notice that 1 = HCF(124,1) .
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Frequently Asked Questions on HCF of 512, 825, 124 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 512, 825, 124?
Answer: HCF of 512, 825, 124 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 825, 124 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 825, 124 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
