Highest Common Factor of 492, 687, 90 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 492, 687, 90 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 492, 687, 90 is 3 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 492, 687, 90 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 492, 687, 90 is 3.
HCF(492, 687, 90) = 3
HCF of 492, 687, 90 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 492, 687, 90 is 3.
Highest Common Factor of 492,687,90 is 3
Step 1: Since 687 > 492, we apply the division lemma to 687 and 492, to get
687 = 492 x 1 + 195
Step 2: Since the reminder 492 ≠ 0, we apply division lemma to 195 and 492, to get
492 = 195 x 2 + 102
Step 3: We consider the new divisor 195 and the new remainder 102, and apply the division lemma to get
195 = 102 x 1 + 93
We consider the new divisor 102 and the new remainder 93,and apply the division lemma to get
102 = 93 x 1 + 9
We consider the new divisor 93 and the new remainder 9,and apply the division lemma to get
93 = 9 x 10 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 492 and 687 is 3
Notice that 3 = HCF(9,3) = HCF(93,9) = HCF(102,93) = HCF(195,102) = HCF(492,195) = HCF(687,492) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 90 > 3, we apply the division lemma to 90 and 3, to get
90 = 3 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 90 is 3
Notice that 3 = HCF(90,3) .
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Frequently Asked Questions on HCF of 492, 687, 90 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 492, 687, 90?
Answer: HCF of 492, 687, 90 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 492, 687, 90 using Euclid's Algorithm?
Answer: For arbitrary numbers 492, 687, 90 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
