Highest Common Factor of 2985, 1098 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 2985, 1098 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2985, 1098 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 2985, 1098 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 2985, 1098 is 3.
HCF(2985, 1098) = 3
HCF of 2985, 1098 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2985, 1098 is 3.
Highest Common Factor of 2985,1098 is 3
Step 1: Since 2985 > 1098, we apply the division lemma to 2985 and 1098, to get
2985 = 1098 x 2 + 789
Step 2: Since the reminder 1098 ≠ 0, we apply division lemma to 789 and 1098, to get
1098 = 789 x 1 + 309
Step 3: We consider the new divisor 789 and the new remainder 309, and apply the division lemma to get
789 = 309 x 2 + 171
We consider the new divisor 309 and the new remainder 171,and apply the division lemma to get
309 = 171 x 1 + 138
We consider the new divisor 171 and the new remainder 138,and apply the division lemma to get
171 = 138 x 1 + 33
We consider the new divisor 138 and the new remainder 33,and apply the division lemma to get
138 = 33 x 4 + 6
We consider the new divisor 33 and the new remainder 6,and apply the division lemma to get
33 = 6 x 5 + 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 2985 and 1098 is 3
Notice that 3 = HCF(6,3) = HCF(33,6) = HCF(138,33) = HCF(171,138) = HCF(309,171) = HCF(789,309) = HCF(1098,789) = HCF(2985,1098) .
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Frequently Asked Questions on HCF of 2985, 1098 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 2985, 1098?
Answer: HCF of 2985, 1098 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2985, 1098 using Euclid's Algorithm?
Answer: For arbitrary numbers 2985, 1098 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.