Highest Common Factor of 306, 136, 730 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 306, 136, 730 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 136, 730 is 2 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 306, 136, 730 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 306, 136, 730 is 2.
HCF(306, 136, 730) = 2
HCF of 306, 136, 730 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 136, 730 is 2.
Highest Common Factor of 306,136,730 is 2
Step 1: Since 306 > 136, we apply the division lemma to 306 and 136, to get
306 = 136 x 2 + 34
Step 2: Since the reminder 136 ≠ 0, we apply division lemma to 34 and 136, to get
136 = 34 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 306 and 136 is 34
Notice that 34 = HCF(136,34) = HCF(306,136) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 730 > 34, we apply the division lemma to 730 and 34, to get
730 = 34 x 21 + 16
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 16 and 34, to get
34 = 16 x 2 + 2
Step 3: We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 34 and 730 is 2
Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(730,34) .
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Frequently Asked Questions on HCF of 306, 136, 730 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 306, 136, 730?
Answer: HCF of 306, 136, 730 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 136, 730 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 136, 730 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.