Highest Common Factor of 354, 4546, 9760 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, 4546, 9760 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 4546, 9760 is 2 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, 4546, 9760 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, 4546, 9760 is 2.
HCF(354, 4546, 9760) = 2
HCF of 354, 4546, 9760 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, 4546, 9760 is 2.
Highest Common Factor of 354,4546,9760 is 2
Step 1: Since 4546 > 354, we apply the division lemma to 4546 and 354, to get
4546 = 354 x 12 + 298
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 298 and 354, to get
354 = 298 x 1 + 56
Step 3: We consider the new divisor 298 and the new remainder 56, and apply the division lemma to get
298 = 56 x 5 + 18
We consider the new divisor 56 and the new remainder 18,and apply the division lemma to get
56 = 18 x 3 + 2
We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get
18 = 2 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 354 and 4546 is 2
Notice that 2 = HCF(18,2) = HCF(56,18) = HCF(298,56) = HCF(354,298) = HCF(4546,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9760 > 2, we apply the division lemma to 9760 and 2, to get
9760 = 2 x 4880 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9760 is 2
Notice that 2 = HCF(9760,2) .
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Frequently Asked Questions on HCF of 354, 4546, 9760 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, 4546, 9760?
Answer: HCF of 354, 4546, 9760 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 4546, 9760 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 4546, 9760 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.