Highest Common Factor of 663, 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 663, 354 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 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 663, 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 663, 354 is 3.
HCF(663, 354) = 3
HCF of 663, 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 663, 354 is 3.
Highest Common Factor of 663,354 is 3
Step 1: Since 663 > 354, we apply the division lemma to 663 and 354, to get
663 = 354 x 1 + 309
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 309 and 354, to get
354 = 309 x 1 + 45
Step 3: We consider the new divisor 309 and the new remainder 45, and apply the division lemma to get
309 = 45 x 6 + 39
We consider the new divisor 45 and the new remainder 39,and apply the division lemma to get
45 = 39 x 1 + 6
We consider the new divisor 39 and the new remainder 6,and apply the division lemma to get
39 = 6 x 6 + 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 663 and 354 is 3
Notice that 3 = HCF(6,3) = HCF(39,6) = HCF(45,39) = HCF(309,45) = HCF(354,309) = HCF(663,354) .
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Frequently Asked Questions on HCF of 663, 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 663, 354?
Answer: HCF of 663, 354 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 354 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 354 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
