Highest Common Factor of 450, 774, 38 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 450, 774, 38 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 450, 774, 38 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 450, 774, 38 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 450, 774, 38 is 2.
HCF(450, 774, 38) = 2
HCF of 450, 774, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 450, 774, 38 is 2.
Highest Common Factor of 450,774,38 is 2
Step 1: Since 774 > 450, we apply the division lemma to 774 and 450, to get
774 = 450 x 1 + 324
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 324 and 450, to get
450 = 324 x 1 + 126
Step 3: We consider the new divisor 324 and the new remainder 126, and apply the division lemma to get
324 = 126 x 2 + 72
We consider the new divisor 126 and the new remainder 72,and apply the division lemma to get
126 = 72 x 1 + 54
We consider the new divisor 72 and the new remainder 54,and apply the division lemma to get
72 = 54 x 1 + 18
We consider the new divisor 54 and the new remainder 18,and apply the division lemma to get
54 = 18 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 450 and 774 is 18
Notice that 18 = HCF(54,18) = HCF(72,54) = HCF(126,72) = HCF(324,126) = HCF(450,324) = HCF(774,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 18, we apply the division lemma to 38 and 18, to get
38 = 18 x 2 + 2
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 2 and 18, to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 38 is 2
Notice that 2 = HCF(18,2) = HCF(38,18) .
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Frequently Asked Questions on HCF of 450, 774, 38 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 450, 774, 38?
Answer: HCF of 450, 774, 38 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 450, 774, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 450, 774, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.