Highest Common Factor of 354, 459, 127, 75 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, 459, 127, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 459, 127, 75 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, 459, 127, 75 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, 459, 127, 75 is 1.
HCF(354, 459, 127, 75) = 1
HCF of 354, 459, 127, 75 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, 459, 127, 75 is 1.
Highest Common Factor of 354,459,127,75 is 1
Step 1: Since 459 > 354, we apply the division lemma to 459 and 354, to get
459 = 354 x 1 + 105
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 105 and 354, to get
354 = 105 x 3 + 39
Step 3: We consider the new divisor 105 and the new remainder 39, and apply the division lemma to get
105 = 39 x 2 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 354 and 459 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(105,39) = HCF(354,105) = HCF(459,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 3, we apply the division lemma to 127 and 3, to get
127 = 3 x 42 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 127 is 1
Notice that 1 = HCF(3,1) = HCF(127,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75 > 1, we apply the division lemma to 75 and 1, to get
75 = 1 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 75 is 1
Notice that 1 = HCF(75,1) .
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Frequently Asked Questions on HCF of 354, 459, 127, 75 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, 459, 127, 75?
Answer: HCF of 354, 459, 127, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 459, 127, 75 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 459, 127, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.