Highest Common Factor of 478, 346, 98 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 478, 346, 98 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 478, 346, 98 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 478, 346, 98 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 478, 346, 98 is 2.
HCF(478, 346, 98) = 2
HCF of 478, 346, 98 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 478, 346, 98 is 2.
Highest Common Factor of 478,346,98 is 2
Step 1: Since 478 > 346, we apply the division lemma to 478 and 346, to get
478 = 346 x 1 + 132
Step 2: Since the reminder 346 ≠ 0, we apply division lemma to 132 and 346, to get
346 = 132 x 2 + 82
Step 3: We consider the new divisor 132 and the new remainder 82, and apply the division lemma to get
132 = 82 x 1 + 50
We consider the new divisor 82 and the new remainder 50,and apply the division lemma to get
82 = 50 x 1 + 32
We consider the new divisor 50 and the new remainder 32,and apply the division lemma to get
50 = 32 x 1 + 18
We consider the new divisor 32 and the new remainder 18,and apply the division lemma to get
32 = 18 x 1 + 14
We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get
18 = 14 x 1 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 478 and 346 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(32,18) = HCF(50,32) = HCF(82,50) = HCF(132,82) = HCF(346,132) = HCF(478,346) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 98 > 2, we apply the division lemma to 98 and 2, to get
98 = 2 x 49 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 98 is 2
Notice that 2 = HCF(98,2) .
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Frequently Asked Questions on HCF of 478, 346, 98 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 478, 346, 98?
Answer: HCF of 478, 346, 98 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 478, 346, 98 using Euclid's Algorithm?
Answer: For arbitrary numbers 478, 346, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.