Highest Common Factor of 300, 742, 774 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 300, 742, 774 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 742, 774 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 300, 742, 774 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 300, 742, 774 is 2.
HCF(300, 742, 774) = 2
HCF of 300, 742, 774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 300, 742, 774 is 2.
Highest Common Factor of 300,742,774 is 2
Step 1: Since 742 > 300, we apply the division lemma to 742 and 300, to get
742 = 300 x 2 + 142
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 142 and 300, to get
300 = 142 x 2 + 16
Step 3: We consider the new divisor 142 and the new remainder 16, and apply the division lemma to get
142 = 16 x 8 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 300 and 742 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(142,16) = HCF(300,142) = HCF(742,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 774 > 2, we apply the division lemma to 774 and 2, to get
774 = 2 x 387 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 774 is 2
Notice that 2 = HCF(774,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 300, 742, 774 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 300, 742, 774?
Answer: HCF of 300, 742, 774 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 742, 774 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 742, 774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
