Highest Common Factor of 354, 915 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, 915 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 915 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 354, 915 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, 915 is 3.
HCF(354, 915) = 3
HCF of 354, 915 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, 915 is 3.
Highest Common Factor of 354,915 is 3
Step 1: Since 915 > 354, we apply the division lemma to 915 and 354, to get
915 = 354 x 2 + 207
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 207 and 354, to get
354 = 207 x 1 + 147
Step 3: We consider the new divisor 207 and the new remainder 147, and apply the division lemma to get
207 = 147 x 1 + 60
We consider the new divisor 147 and the new remainder 60,and apply the division lemma to get
147 = 60 x 2 + 27
We consider the new divisor 60 and the new remainder 27,and apply the division lemma to get
60 = 27 x 2 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 354 and 915 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(60,27) = HCF(147,60) = HCF(207,147) = HCF(354,207) = HCF(915,354) .
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Frequently Asked Questions on HCF of 354, 915 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, 915?
Answer: HCF of 354, 915 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 915 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 915 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.