Highest Common Factor of 219, 354 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 219, 354 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 219, 354 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 219, 354 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 219, 354 is 3.
HCF(219, 354) = 3
HCF of 219, 354 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 219, 354 is 3.
Highest Common Factor of 219,354 is 3
Step 1: Since 354 > 219, we apply the division lemma to 354 and 219, to get
354 = 219 x 1 + 135
Step 2: Since the reminder 219 ≠ 0, we apply division lemma to 135 and 219, to get
219 = 135 x 1 + 84
Step 3: We consider the new divisor 135 and the new remainder 84, and apply the division lemma to get
135 = 84 x 1 + 51
We consider the new divisor 84 and the new remainder 51,and apply the division lemma to get
84 = 51 x 1 + 33
We consider the new divisor 51 and the new remainder 33,and apply the division lemma to get
51 = 33 x 1 + 18
We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get
33 = 18 x 1 + 15
We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get
18 = 15 x 1 + 3
We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 219 and 354 is 3
Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(51,33) = HCF(84,51) = HCF(135,84) = HCF(219,135) = HCF(354,219) .
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Frequently Asked Questions on HCF of 219, 354 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 219, 354?
Answer: HCF of 219, 354 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 219, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 219, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.