Highest Common Factor of 442, 742, 78 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 442, 742, 78 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 442, 742, 78 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 442, 742, 78 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 442, 742, 78 is 2.
HCF(442, 742, 78) = 2
HCF of 442, 742, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 442, 742, 78 is 2.
Highest Common Factor of 442,742,78 is 2
Step 1: Since 742 > 442, we apply the division lemma to 742 and 442, to get
742 = 442 x 1 + 300
Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 300 and 442, to get
442 = 300 x 1 + 142
Step 3: We consider the new divisor 300 and the new remainder 142, and apply the division lemma to get
300 = 142 x 2 + 16
We consider the new divisor 142 and the new remainder 16,and apply the division lemma to get
142 = 16 x 8 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 442 and 742 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(142,16) = HCF(300,142) = HCF(442,300) = HCF(742,442) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 2, we apply the division lemma to 78 and 2, to get
78 = 2 x 39 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 78 is 2
Notice that 2 = HCF(78,2) .
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Frequently Asked Questions on HCF of 442, 742, 78 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 442, 742, 78?
Answer: HCF of 442, 742, 78 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 442, 742, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 442, 742, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.