Highest Common Factor of 36, 90, 420, 185 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 36, 90, 420, 185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 36, 90, 420, 185 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 36, 90, 420, 185 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 36, 90, 420, 185 is 1.
HCF(36, 90, 420, 185) = 1
HCF of 36, 90, 420, 185 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 36, 90, 420, 185 is 1.
Highest Common Factor of 36,90,420,185 is 1
Step 1: Since 90 > 36, we apply the division lemma to 90 and 36, to get
90 = 36 x 2 + 18
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 18 and 36, to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 36 and 90 is 18
Notice that 18 = HCF(36,18) = HCF(90,36) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 420 > 18, we apply the division lemma to 420 and 18, to get
420 = 18 x 23 + 6
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 6 and 18, to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 18 and 420 is 6
Notice that 6 = HCF(18,6) = HCF(420,18) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 185 > 6, we apply the division lemma to 185 and 6, to get
185 = 6 x 30 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 185 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(185,6) .
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Frequently Asked Questions on HCF of 36, 90, 420, 185 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 36, 90, 420, 185?
Answer: HCF of 36, 90, 420, 185 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 36, 90, 420, 185 using Euclid's Algorithm?
Answer: For arbitrary numbers 36, 90, 420, 185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.