Highest Common Factor of 774, 300 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 774, 300 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 300 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 774, 300 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 774, 300 is 6.
HCF(774, 300) = 6
HCF of 774, 300 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 300 is 6.
Highest Common Factor of 774,300 is 6
Step 1: Since 774 > 300, we apply the division lemma to 774 and 300, to get
774 = 300 x 2 + 174
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 174 and 300, to get
300 = 174 x 1 + 126
Step 3: We consider the new divisor 174 and the new remainder 126, and apply the division lemma to get
174 = 126 x 1 + 48
We consider the new divisor 126 and the new remainder 48,and apply the division lemma to get
126 = 48 x 2 + 30
We consider the new divisor 48 and the new remainder 30,and apply the division lemma to get
48 = 30 x 1 + 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 774 and 300 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(48,30) = HCF(126,48) = HCF(174,126) = HCF(300,174) = HCF(774,300) .
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Frequently Asked Questions on HCF of 774, 300 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 774, 300?
Answer: HCF of 774, 300 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 300 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 300 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.