Highest Common Factor of 354, 302, 365, 55 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 354, 302, 365, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 302, 365, 55 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 354, 302, 365, 55 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 354, 302, 365, 55 is 1.
HCF(354, 302, 365, 55) = 1
HCF of 354, 302, 365, 55 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 302, 365, 55 is 1.
Highest Common Factor of 354,302,365,55 is 1
Step 1: Since 354 > 302, we apply the division lemma to 354 and 302, to get
354 = 302 x 1 + 52
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 52 and 302, to get
302 = 52 x 5 + 42
Step 3: We consider the new divisor 52 and the new remainder 42, and apply the division lemma to get
52 = 42 x 1 + 10
We consider the new divisor 42 and the new remainder 10,and apply the division lemma to get
42 = 10 x 4 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 302 is 2
Notice that 2 = HCF(10,2) = HCF(42,10) = HCF(52,42) = HCF(302,52) = HCF(354,302) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 365 > 2, we apply the division lemma to 365 and 2, to get
365 = 2 x 182 + 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 365 is 1
Notice that 1 = HCF(2,1) = HCF(365,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 55 > 1, we apply the division lemma to 55 and 1, to get
55 = 1 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 55 is 1
Notice that 1 = HCF(55,1) .
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Frequently Asked Questions on HCF of 354, 302, 365, 55 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 354, 302, 365, 55?
Answer: HCF of 354, 302, 365, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 302, 365, 55 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 302, 365, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.