Highest Common Factor of 750, 306 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 750, 306 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 306 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 750, 306 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 750, 306 is 6.
HCF(750, 306) = 6
HCF of 750, 306 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 750, 306 is 6.
Highest Common Factor of 750,306 is 6
Step 1: Since 750 > 306, we apply the division lemma to 750 and 306, to get
750 = 306 x 2 + 138
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 138 and 306, to get
306 = 138 x 2 + 30
Step 3: We consider the new divisor 138 and the new remainder 30, and apply the division lemma to get
138 = 30 x 4 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 750 and 306 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(138,30) = HCF(306,138) = HCF(750,306) .
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Frequently Asked Questions on HCF of 750, 306 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 750, 306?
Answer: HCF of 750, 306 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 306 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 306 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.