Highest Common Factor of 906, 498, 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 906, 498, 36 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 906, 498, 36 is 6 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 906, 498, 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 906, 498, 36 is 6.
HCF(906, 498, 36) = 6
HCF of 906, 498, 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 906, 498, 36 is 6.
Highest Common Factor of 906,498,36 is 6
Step 1: Since 906 > 498, we apply the division lemma to 906 and 498, to get
906 = 498 x 1 + 408
Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 408 and 498, to get
498 = 408 x 1 + 90
Step 3: We consider the new divisor 408 and the new remainder 90, and apply the division lemma to get
408 = 90 x 4 + 48
We consider the new divisor 90 and the new remainder 48,and apply the division lemma to get
90 = 48 x 1 + 42
We consider the new divisor 48 and the new remainder 42,and apply the division lemma to get
48 = 42 x 1 + 6
We consider the new divisor 42 and the new remainder 6,and apply the division lemma to get
42 = 6 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 906 and 498 is 6
Notice that 6 = HCF(42,6) = HCF(48,42) = HCF(90,48) = HCF(408,90) = HCF(498,408) = HCF(906,498) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 36 > 6, we apply the division lemma to 36 and 6, to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 36 is 6
Notice that 6 = HCF(36,6) .
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Frequently Asked Questions on HCF of 906, 498, 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 906, 498, 36?
Answer: HCF of 906, 498, 36 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 906, 498, 36 using Euclid's Algorithm?
Answer: For arbitrary numbers 906, 498, 36 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.