Highest Common Factor of 825, 176, 408 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, 176, 408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 825, 176, 408 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, 176, 408 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, 176, 408 is 1.
HCF(825, 176, 408) = 1
HCF of 825, 176, 408 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, 176, 408 is 1.
Highest Common Factor of 825,176,408 is 1
Step 1: Since 825 > 176, we apply the division lemma to 825 and 176, to get
825 = 176 x 4 + 121
Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 121 and 176, to get
176 = 121 x 1 + 55
Step 3: We consider the new divisor 121 and the new remainder 55, and apply the division lemma to get
121 = 55 x 2 + 11
We consider the new divisor 55 and the new remainder 11, and apply the division lemma to get
55 = 11 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 825 and 176 is 11
Notice that 11 = HCF(55,11) = HCF(121,55) = HCF(176,121) = HCF(825,176) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 408 > 11, we apply the division lemma to 408 and 11, to get
408 = 11 x 37 + 1
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 1 and 11, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 408 is 1
Notice that 1 = HCF(11,1) = HCF(408,11) .
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Frequently Asked Questions on HCF of 825, 176, 408 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, 176, 408?
Answer: HCF of 825, 176, 408 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 825, 176, 408 using Euclid's Algorithm?
Answer: For arbitrary numbers 825, 176, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.