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 998, 6105, 2639 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 6105, 2639 is 1 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 998, 6105, 2639 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 998, 6105, 2639 is 1.
HCF(998, 6105, 2639) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 6105, 2639 is 1.
Step 1: Since 6105 > 998, we apply the division lemma to 6105 and 998, to get
6105 = 998 x 6 + 117
Step 2: Since the reminder 998 ≠ 0, we apply division lemma to 117 and 998, to get
998 = 117 x 8 + 62
Step 3: We consider the new divisor 117 and the new remainder 62, and apply the division lemma to get
117 = 62 x 1 + 55
We consider the new divisor 62 and the new remainder 55,and apply the division lemma to get
62 = 55 x 1 + 7
We consider the new divisor 55 and the new remainder 7,and apply the division lemma to get
55 = 7 x 7 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 998 and 6105 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(55,7) = HCF(62,55) = HCF(117,62) = HCF(998,117) = HCF(6105,998) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2639 > 1, we apply the division lemma to 2639 and 1, to get
2639 = 1 x 2639 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2639 is 1
Notice that 1 = HCF(2639,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 998, 6105, 2639?
Answer: HCF of 998, 6105, 2639 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 6105, 2639 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 6105, 2639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.