Highest Common Factor of 754, 420 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 754, 420 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 420 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 754, 420 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 754, 420 is 2.
HCF(754, 420) = 2
HCF of 754, 420 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 420 is 2.
Highest Common Factor of 754,420 is 2
Step 1: Since 754 > 420, we apply the division lemma to 754 and 420, to get
754 = 420 x 1 + 334
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 334 and 420, to get
420 = 334 x 1 + 86
Step 3: We consider the new divisor 334 and the new remainder 86, and apply the division lemma to get
334 = 86 x 3 + 76
We consider the new divisor 86 and the new remainder 76,and apply the division lemma to get
86 = 76 x 1 + 10
We consider the new divisor 76 and the new remainder 10,and apply the division lemma to get
76 = 10 x 7 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 754 and 420 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(76,10) = HCF(86,76) = HCF(334,86) = HCF(420,334) = HCF(754,420) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 754, 420 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 754, 420?
Answer: HCF of 754, 420 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.