Highest Common Factor of 428, 742, 100 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 428, 742, 100 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 742, 100 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 428, 742, 100 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 428, 742, 100 is 2.
HCF(428, 742, 100) = 2
HCF of 428, 742, 100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 742, 100 is 2.
Highest Common Factor of 428,742,100 is 2
Step 1: Since 742 > 428, we apply the division lemma to 742 and 428, to get
742 = 428 x 1 + 314
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 314 and 428, to get
428 = 314 x 1 + 114
Step 3: We consider the new divisor 314 and the new remainder 114, and apply the division lemma to get
314 = 114 x 2 + 86
We consider the new divisor 114 and the new remainder 86,and apply the division lemma to get
114 = 86 x 1 + 28
We consider the new divisor 86 and the new remainder 28,and apply the division lemma to get
86 = 28 x 3 + 2
We consider the new divisor 28 and the new remainder 2,and apply the division lemma to get
28 = 2 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 428 and 742 is 2
Notice that 2 = HCF(28,2) = HCF(86,28) = HCF(114,86) = HCF(314,114) = HCF(428,314) = HCF(742,428) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 100 > 2, we apply the division lemma to 100 and 2, to get
100 = 2 x 50 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 100 is 2
Notice that 2 = HCF(100,2) .
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Frequently Asked Questions on HCF of 428, 742, 100 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 428, 742, 100?
Answer: HCF of 428, 742, 100 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 742, 100 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 742, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.