Highest Common Factor of 306, 1998 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 306, 1998 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 1998 is 18 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 306, 1998 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 306, 1998 is 18.
HCF(306, 1998) = 18
HCF of 306, 1998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 1998 is 18.
Highest Common Factor of 306,1998 is 18
Step 1: Since 1998 > 306, we apply the division lemma to 1998 and 306, to get
1998 = 306 x 6 + 162
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 162 and 306, to get
306 = 162 x 1 + 144
Step 3: We consider the new divisor 162 and the new remainder 144, and apply the division lemma to get
162 = 144 x 1 + 18
We consider the new divisor 144 and the new remainder 18, and apply the division lemma to get
144 = 18 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 306 and 1998 is 18
Notice that 18 = HCF(144,18) = HCF(162,144) = HCF(306,162) = HCF(1998,306) .
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Frequently Asked Questions on HCF of 306, 1998 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 306, 1998?
Answer: HCF of 306, 1998 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 1998 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 1998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.