Highest Common Factor of 1572, 7140, 74774 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 1572, 7140, 74774 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1572, 7140, 74774 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 1572, 7140, 74774 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 1572, 7140, 74774 is 2.
HCF(1572, 7140, 74774) = 2
HCF of 1572, 7140, 74774 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1572, 7140, 74774 is 2.
Highest Common Factor of 1572,7140,74774 is 2
Step 1: Since 7140 > 1572, we apply the division lemma to 7140 and 1572, to get
7140 = 1572 x 4 + 852
Step 2: Since the reminder 1572 ≠ 0, we apply division lemma to 852 and 1572, to get
1572 = 852 x 1 + 720
Step 3: We consider the new divisor 852 and the new remainder 720, and apply the division lemma to get
852 = 720 x 1 + 132
We consider the new divisor 720 and the new remainder 132,and apply the division lemma to get
720 = 132 x 5 + 60
We consider the new divisor 132 and the new remainder 60,and apply the division lemma to get
132 = 60 x 2 + 12
We consider the new divisor 60 and the new remainder 12,and apply the division lemma to get
60 = 12 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 1572 and 7140 is 12
Notice that 12 = HCF(60,12) = HCF(132,60) = HCF(720,132) = HCF(852,720) = HCF(1572,852) = HCF(7140,1572) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74774 > 12, we apply the division lemma to 74774 and 12, to get
74774 = 12 x 6231 + 2
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 74774 is 2
Notice that 2 = HCF(12,2) = HCF(74774,12) .
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Frequently Asked Questions on HCF of 1572, 7140, 74774 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 1572, 7140, 74774?
Answer: HCF of 1572, 7140, 74774 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1572, 7140, 74774 using Euclid's Algorithm?
Answer: For arbitrary numbers 1572, 7140, 74774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
