Highest Common Factor of 355, 478 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 355, 478 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 355, 478 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 355, 478 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 355, 478 is 1.
HCF(355, 478) = 1
HCF of 355, 478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 355, 478 is 1.
Highest Common Factor of 355,478 is 1
Step 1: Since 478 > 355, we apply the division lemma to 478 and 355, to get
478 = 355 x 1 + 123
Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 123 and 355, to get
355 = 123 x 2 + 109
Step 3: We consider the new divisor 123 and the new remainder 109, and apply the division lemma to get
123 = 109 x 1 + 14
We consider the new divisor 109 and the new remainder 14,and apply the division lemma to get
109 = 14 x 7 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
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 355 and 478 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(109,14) = HCF(123,109) = HCF(355,123) = HCF(478,355) .
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Frequently Asked Questions on HCF of 355, 478 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 355, 478?
Answer: HCF of 355, 478 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 355, 478 using Euclid's Algorithm?
Answer: For arbitrary numbers 355, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.