Highest Common Factor of 748, 1436, 3005 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 748, 1436, 3005 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 1436, 3005 is 1 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 748, 1436, 3005 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 748, 1436, 3005 is 1.
HCF(748, 1436, 3005) = 1
HCF of 748, 1436, 3005 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 1436, 3005 is 1.
Highest Common Factor of 748,1436,3005 is 1
Step 1: Since 1436 > 748, we apply the division lemma to 1436 and 748, to get
1436 = 748 x 1 + 688
Step 2: Since the reminder 748 ≠ 0, we apply division lemma to 688 and 748, to get
748 = 688 x 1 + 60
Step 3: We consider the new divisor 688 and the new remainder 60, and apply the division lemma to get
688 = 60 x 11 + 28
We consider the new divisor 60 and the new remainder 28,and apply the division lemma to get
60 = 28 x 2 + 4
We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 748 and 1436 is 4
Notice that 4 = HCF(28,4) = HCF(60,28) = HCF(688,60) = HCF(748,688) = HCF(1436,748) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3005 > 4, we apply the division lemma to 3005 and 4, to get
3005 = 4 x 751 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 3005 is 1
Notice that 1 = HCF(4,1) = HCF(3005,4) .
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Frequently Asked Questions on HCF of 748, 1436, 3005 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 748, 1436, 3005?
Answer: HCF of 748, 1436, 3005 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 1436, 3005 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 1436, 3005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.