Highest Common Factor of 300, 64, 112, 734 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, 64, 112, 734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 64, 112, 734 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, 64, 112, 734 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, 64, 112, 734 is 2.
HCF(300, 64, 112, 734) = 2
HCF of 300, 64, 112, 734 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, 64, 112, 734 is 2.
Highest Common Factor of 300,64,112,734 is 2
Step 1: Since 300 > 64, we apply the division lemma to 300 and 64, to get
300 = 64 x 4 + 44
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 44 and 64, to get
64 = 44 x 1 + 20
Step 3: We consider the new divisor 44 and the new remainder 20, and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4, and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 300 and 64 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(64,44) = HCF(300,64) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 4, we apply the division lemma to 112 and 4, to get
112 = 4 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 112 is 4
Notice that 4 = HCF(112,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 734 > 4, we apply the division lemma to 734 and 4, to get
734 = 4 x 183 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 734 is 2
Notice that 2 = HCF(4,2) = HCF(734,4) .
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Frequently Asked Questions on HCF of 300, 64, 112, 734 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, 64, 112, 734?
Answer: HCF of 300, 64, 112, 734 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 64, 112, 734 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 64, 112, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.