Highest Common Factor of 7566, 1602 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 7566, 1602 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 7566, 1602 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 7566, 1602 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 7566, 1602 is 6.
HCF(7566, 1602) = 6
HCF of 7566, 1602 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7566, 1602 is 6.
Highest Common Factor of 7566,1602 is 6
Step 1: Since 7566 > 1602, we apply the division lemma to 7566 and 1602, to get
7566 = 1602 x 4 + 1158
Step 2: Since the reminder 1602 ≠ 0, we apply division lemma to 1158 and 1602, to get
1602 = 1158 x 1 + 444
Step 3: We consider the new divisor 1158 and the new remainder 444, and apply the division lemma to get
1158 = 444 x 2 + 270
We consider the new divisor 444 and the new remainder 270,and apply the division lemma to get
444 = 270 x 1 + 174
We consider the new divisor 270 and the new remainder 174,and apply the division lemma to get
270 = 174 x 1 + 96
We consider the new divisor 174 and the new remainder 96,and apply the division lemma to get
174 = 96 x 1 + 78
We consider the new divisor 96 and the new remainder 78,and apply the division lemma to get
96 = 78 x 1 + 18
We consider the new divisor 78 and the new remainder 18,and apply the division lemma to get
78 = 18 x 4 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 7566 and 1602 is 6
Notice that 6 = HCF(18,6) = HCF(78,18) = HCF(96,78) = HCF(174,96) = HCF(270,174) = HCF(444,270) = HCF(1158,444) = HCF(1602,1158) = HCF(7566,1602) .
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Frequently Asked Questions on HCF of 7566, 1602 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 7566, 1602?
Answer: HCF of 7566, 1602 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7566, 1602 using Euclid's Algorithm?
Answer: For arbitrary numbers 7566, 1602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.