Highest Common Factor of 496, 178, 421, 546 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 496, 178, 421, 546 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 496, 178, 421, 546 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 496, 178, 421, 546 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 496, 178, 421, 546 is 1.
HCF(496, 178, 421, 546) = 1
HCF of 496, 178, 421, 546 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 496, 178, 421, 546 is 1.
Highest Common Factor of 496,178,421,546 is 1
Step 1: Since 496 > 178, we apply the division lemma to 496 and 178, to get
496 = 178 x 2 + 140
Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 140 and 178, to get
178 = 140 x 1 + 38
Step 3: We consider the new divisor 140 and the new remainder 38, and apply the division lemma to get
140 = 38 x 3 + 26
We consider the new divisor 38 and the new remainder 26,and apply the division lemma to get
38 = 26 x 1 + 12
We consider the new divisor 26 and the new remainder 12,and apply the division lemma to get
26 = 12 x 2 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 496 and 178 is 2
Notice that 2 = HCF(12,2) = HCF(26,12) = HCF(38,26) = HCF(140,38) = HCF(178,140) = HCF(496,178) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 2, we apply the division lemma to 421 and 2, to get
421 = 2 x 210 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 421 is 1
Notice that 1 = HCF(2,1) = HCF(421,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 546 > 1, we apply the division lemma to 546 and 1, to get
546 = 1 x 546 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 546 is 1
Notice that 1 = HCF(546,1) .
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Frequently Asked Questions on HCF of 496, 178, 421, 546 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 496, 178, 421, 546?
Answer: HCF of 496, 178, 421, 546 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 496, 178, 421, 546 using Euclid's Algorithm?
Answer: For arbitrary numbers 496, 178, 421, 546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
