Highest Common Factor of 275, 400, 338 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 275, 400, 338 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 275, 400, 338 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 275, 400, 338 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 275, 400, 338 is 1.
HCF(275, 400, 338) = 1
HCF of 275, 400, 338 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 275, 400, 338 is 1.
Highest Common Factor of 275,400,338 is 1
Step 1: Since 400 > 275, we apply the division lemma to 400 and 275, to get
400 = 275 x 1 + 125
Step 2: Since the reminder 275 ≠ 0, we apply division lemma to 125 and 275, to get
275 = 125 x 2 + 25
Step 3: We consider the new divisor 125 and the new remainder 25, and apply the division lemma to get
125 = 25 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 275 and 400 is 25
Notice that 25 = HCF(125,25) = HCF(275,125) = HCF(400,275) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 338 > 25, we apply the division lemma to 338 and 25, to get
338 = 25 x 13 + 13
Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 13 and 25, to get
25 = 13 x 1 + 12
Step 3: We consider the new divisor 13 and the new remainder 12, and apply the division lemma to get
13 = 12 x 1 + 1
We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get
12 = 1 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 25 and 338 is 1
Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(25,13) = HCF(338,25) .
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Frequently Asked Questions on HCF of 275, 400, 338 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 275, 400, 338?
Answer: HCF of 275, 400, 338 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 275, 400, 338 using Euclid's Algorithm?
Answer: For arbitrary numbers 275, 400, 338 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.