Highest Common Factor of 742, 7876, 8608 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 742, 7876, 8608 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 7876, 8608 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 742, 7876, 8608 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 742, 7876, 8608 is 2.
HCF(742, 7876, 8608) = 2
HCF of 742, 7876, 8608 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 7876, 8608 is 2.
Highest Common Factor of 742,7876,8608 is 2
Step 1: Since 7876 > 742, we apply the division lemma to 7876 and 742, to get
7876 = 742 x 10 + 456
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 456 and 742, to get
742 = 456 x 1 + 286
Step 3: We consider the new divisor 456 and the new remainder 286, and apply the division lemma to get
456 = 286 x 1 + 170
We consider the new divisor 286 and the new remainder 170,and apply the division lemma to get
286 = 170 x 1 + 116
We consider the new divisor 170 and the new remainder 116,and apply the division lemma to get
170 = 116 x 1 + 54
We consider the new divisor 116 and the new remainder 54,and apply the division lemma to get
116 = 54 x 2 + 8
We consider the new divisor 54 and the new remainder 8,and apply the division lemma to get
54 = 8 x 6 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 742 and 7876 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(54,8) = HCF(116,54) = HCF(170,116) = HCF(286,170) = HCF(456,286) = HCF(742,456) = HCF(7876,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8608 > 2, we apply the division lemma to 8608 and 2, to get
8608 = 2 x 4304 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 8608 is 2
Notice that 2 = HCF(8608,2) .
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Frequently Asked Questions on HCF of 742, 7876, 8608 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 742, 7876, 8608?
Answer: HCF of 742, 7876, 8608 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 7876, 8608 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 7876, 8608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.