Highest Common Factor of 369, 998, 990 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 369, 998, 990 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 369, 998, 990 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 369, 998, 990 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 369, 998, 990 is 1.
HCF(369, 998, 990) = 1
HCF of 369, 998, 990 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 369, 998, 990 is 1.
Highest Common Factor of 369,998,990 is 1
Step 1: Since 998 > 369, we apply the division lemma to 998 and 369, to get
998 = 369 x 2 + 260
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 260 and 369, to get
369 = 260 x 1 + 109
Step 3: We consider the new divisor 260 and the new remainder 109, and apply the division lemma to get
260 = 109 x 2 + 42
We consider the new divisor 109 and the new remainder 42,and apply the division lemma to get
109 = 42 x 2 + 25
We consider the new divisor 42 and the new remainder 25,and apply the division lemma to get
42 = 25 x 1 + 17
We consider the new divisor 25 and the new remainder 17,and apply the division lemma to get
25 = 17 x 1 + 8
We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get
17 = 8 x 2 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 369 and 998 is 1
Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(25,17) = HCF(42,25) = HCF(109,42) = HCF(260,109) = HCF(369,260) = HCF(998,369) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 990 > 1, we apply the division lemma to 990 and 1, to get
990 = 1 x 990 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 990 is 1
Notice that 1 = HCF(990,1) .
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Frequently Asked Questions on HCF of 369, 998, 990 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 369, 998, 990?
Answer: HCF of 369, 998, 990 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 369, 998, 990 using Euclid's Algorithm?
Answer: For arbitrary numbers 369, 998, 990 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.