Highest Common Factor of 490, 735, 612 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 490, 735, 612 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 490, 735, 612 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 490, 735, 612 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 490, 735, 612 is 1.
HCF(490, 735, 612) = 1
HCF of 490, 735, 612 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 490, 735, 612 is 1.
Highest Common Factor of 490,735,612 is 1
Step 1: Since 735 > 490, we apply the division lemma to 735 and 490, to get
735 = 490 x 1 + 245
Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 245 and 490, to get
490 = 245 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 245, the HCF of 490 and 735 is 245
Notice that 245 = HCF(490,245) = HCF(735,490) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 612 > 245, we apply the division lemma to 612 and 245, to get
612 = 245 x 2 + 122
Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 122 and 245, to get
245 = 122 x 2 + 1
Step 3: We consider the new divisor 122 and the new remainder 1, and apply the division lemma to get
122 = 1 x 122 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 245 and 612 is 1
Notice that 1 = HCF(122,1) = HCF(245,122) = HCF(612,245) .
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Frequently Asked Questions on HCF of 490, 735, 612 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 490, 735, 612?
Answer: HCF of 490, 735, 612 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 490, 735, 612 using Euclid's Algorithm?
Answer: For arbitrary numbers 490, 735, 612 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.