Highest Common Factor of 998, 409, 900, 36 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 998, 409, 900, 36 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 998, 409, 900, 36 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, 409, 900, 36 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, 409, 900, 36 is 1.
HCF(998, 409, 900, 36) = 1
HCF of 998, 409, 900, 36 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 998, 409, 900, 36 is 1.
Highest Common Factor of 998,409,900,36 is 1
Step 1: Since 998 > 409, we apply the division lemma to 998 and 409, to get
998 = 409 x 2 + 180
Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 180 and 409, to get
409 = 180 x 2 + 49
Step 3: We consider the new divisor 180 and the new remainder 49, and apply the division lemma to get
180 = 49 x 3 + 33
We consider the new divisor 49 and the new remainder 33,and apply the division lemma to get
49 = 33 x 1 + 16
We consider the new divisor 33 and the new remainder 16,and apply the division lemma to get
33 = 16 x 2 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 998 and 409 is 1
Notice that 1 = HCF(16,1) = HCF(33,16) = HCF(49,33) = HCF(180,49) = HCF(409,180) = HCF(998,409) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 900 > 1, we apply the division lemma to 900 and 1, to get
900 = 1 x 900 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 900 is 1
Notice that 1 = HCF(900,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 1, we apply the division lemma to 36 and 1, to get
36 = 1 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 36 is 1
Notice that 1 = HCF(36,1) .
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Frequently Asked Questions on HCF of 998, 409, 900, 36 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 998, 409, 900, 36?
Answer: HCF of 998, 409, 900, 36 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 998, 409, 900, 36 using Euclid's Algorithm?
Answer: For arbitrary numbers 998, 409, 900, 36 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.