Highest Common Factor of 357, 135, 54 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 357, 135, 54 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 357, 135, 54 is 3 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 357, 135, 54 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 357, 135, 54 is 3.
HCF(357, 135, 54) = 3
HCF of 357, 135, 54 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 357, 135, 54 is 3.
Highest Common Factor of 357,135,54 is 3
Step 1: Since 357 > 135, we apply the division lemma to 357 and 135, to get
357 = 135 x 2 + 87
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 87 and 135, to get
135 = 87 x 1 + 48
Step 3: We consider the new divisor 87 and the new remainder 48, and apply the division lemma to get
87 = 48 x 1 + 39
We consider the new divisor 48 and the new remainder 39,and apply the division lemma to get
48 = 39 x 1 + 9
We consider the new divisor 39 and the new remainder 9,and apply the division lemma to get
39 = 9 x 4 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 357 and 135 is 3
Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(48,39) = HCF(87,48) = HCF(135,87) = HCF(357,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 3, we apply the division lemma to 54 and 3, to get
54 = 3 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 54 is 3
Notice that 3 = HCF(54,3) .
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Frequently Asked Questions on HCF of 357, 135, 54 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 357, 135, 54?
Answer: HCF of 357, 135, 54 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 357, 135, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 357, 135, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.