Highest Common Factor of 742, 4714 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, 4714 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 4714 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, 4714 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, 4714 is 2.
HCF(742, 4714) = 2
HCF of 742, 4714 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, 4714 is 2.
Highest Common Factor of 742,4714 is 2
Step 1: Since 4714 > 742, we apply the division lemma to 4714 and 742, to get
4714 = 742 x 6 + 262
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 262 and 742, to get
742 = 262 x 2 + 218
Step 3: We consider the new divisor 262 and the new remainder 218, and apply the division lemma to get
262 = 218 x 1 + 44
We consider the new divisor 218 and the new remainder 44,and apply the division lemma to get
218 = 44 x 4 + 42
We consider the new divisor 44 and the new remainder 42,and apply the division lemma to get
44 = 42 x 1 + 2
We consider the new divisor 42 and the new remainder 2,and apply the division lemma to get
42 = 2 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 742 and 4714 is 2
Notice that 2 = HCF(42,2) = HCF(44,42) = HCF(218,44) = HCF(262,218) = HCF(742,262) = HCF(4714,742) .
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Frequently Asked Questions on HCF of 742, 4714 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, 4714?
Answer: HCF of 742, 4714 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 4714 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 4714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.