Highest Common Factor of 354, 600 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, 600 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 600 is 6 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, 600 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, 600 is 6.
HCF(354, 600) = 6
HCF of 354, 600 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, 600 is 6.
Highest Common Factor of 354,600 is 6
Step 1: Since 600 > 354, we apply the division lemma to 600 and 354, to get
600 = 354 x 1 + 246
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 246 and 354, to get
354 = 246 x 1 + 108
Step 3: We consider the new divisor 246 and the new remainder 108, and apply the division lemma to get
246 = 108 x 2 + 30
We consider the new divisor 108 and the new remainder 30,and apply the division lemma to get
108 = 30 x 3 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 354 and 600 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(108,30) = HCF(246,108) = HCF(354,246) = HCF(600,354) .
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Frequently Asked Questions on HCF of 354, 600 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, 600?
Answer: HCF of 354, 600 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.