Highest Common Factor of 338, 552, 600 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 338, 552, 600 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 552, 600 is 2 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 338, 552, 600 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 338, 552, 600 is 2.
HCF(338, 552, 600) = 2
HCF of 338, 552, 600 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 338, 552, 600 is 2.
Highest Common Factor of 338,552,600 is 2
Step 1: Since 552 > 338, we apply the division lemma to 552 and 338, to get
552 = 338 x 1 + 214
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 214 and 338, to get
338 = 214 x 1 + 124
Step 3: We consider the new divisor 214 and the new remainder 124, and apply the division lemma to get
214 = 124 x 1 + 90
We consider the new divisor 124 and the new remainder 90,and apply the division lemma to get
124 = 90 x 1 + 34
We consider the new divisor 90 and the new remainder 34,and apply the division lemma to get
90 = 34 x 2 + 22
We consider the new divisor 34 and the new remainder 22,and apply the division lemma to get
34 = 22 x 1 + 12
We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get
22 = 12 x 1 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 338 and 552 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(34,22) = HCF(90,34) = HCF(124,90) = HCF(214,124) = HCF(338,214) = HCF(552,338) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 600 > 2, we apply the division lemma to 600 and 2, to get
600 = 2 x 300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 600 is 2
Notice that 2 = HCF(600,2) .
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Frequently Asked Questions on HCF of 338, 552, 600 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 338, 552, 600?
Answer: HCF of 338, 552, 600 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 552, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 552, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.