Highest Common Factor of 546, 931, 450 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 546, 931, 450 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 546, 931, 450 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 546, 931, 450 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 546, 931, 450 is 1.
HCF(546, 931, 450) = 1
HCF of 546, 931, 450 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 546, 931, 450 is 1.
Highest Common Factor of 546,931,450 is 1
Step 1: Since 931 > 546, we apply the division lemma to 931 and 546, to get
931 = 546 x 1 + 385
Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 385 and 546, to get
546 = 385 x 1 + 161
Step 3: We consider the new divisor 385 and the new remainder 161, and apply the division lemma to get
385 = 161 x 2 + 63
We consider the new divisor 161 and the new remainder 63,and apply the division lemma to get
161 = 63 x 2 + 35
We consider the new divisor 63 and the new remainder 35,and apply the division lemma to get
63 = 35 x 1 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 546 and 931 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(63,35) = HCF(161,63) = HCF(385,161) = HCF(546,385) = HCF(931,546) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 450 > 7, we apply the division lemma to 450 and 7, to get
450 = 7 x 64 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: 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 7 and 450 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(450,7) .
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Frequently Asked Questions on HCF of 546, 931, 450 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 546, 931, 450?
Answer: HCF of 546, 931, 450 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 546, 931, 450 using Euclid's Algorithm?
Answer: For arbitrary numbers 546, 931, 450 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
