Highest Common Factor of 718, 998 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 718, 998 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 718, 998 is 2 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 718, 998 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 718, 998 is 2.
HCF(718, 998) = 2
HCF of 718, 998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 718, 998 is 2.
Highest Common Factor of 718,998 is 2
Step 1: Since 998 > 718, we apply the division lemma to 998 and 718, to get
998 = 718 x 1 + 280
Step 2: Since the reminder 718 ≠ 0, we apply division lemma to 280 and 718, to get
718 = 280 x 2 + 158
Step 3: We consider the new divisor 280 and the new remainder 158, and apply the division lemma to get
280 = 158 x 1 + 122
We consider the new divisor 158 and the new remainder 122,and apply the division lemma to get
158 = 122 x 1 + 36
We consider the new divisor 122 and the new remainder 36,and apply the division lemma to get
122 = 36 x 3 + 14
We consider the new divisor 36 and the new remainder 14,and apply the division lemma to get
36 = 14 x 2 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 718 and 998 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(36,14) = HCF(122,36) = HCF(158,122) = HCF(280,158) = HCF(718,280) = HCF(998,718) .
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Frequently Asked Questions on HCF of 718, 998 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 718, 998?
Answer: HCF of 718, 998 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 718, 998 using Euclid's Algorithm?
Answer: For arbitrary numbers 718, 998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
