Highest Common Factor of 295, 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 295, 420 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 295, 420 is 5 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 295, 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 295, 420 is 5.
HCF(295, 420) = 5
HCF of 295, 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 295, 420 is 5.
Highest Common Factor of 295,420 is 5
Step 1: Since 420 > 295, we apply the division lemma to 420 and 295, to get
420 = 295 x 1 + 125
Step 2: Since the reminder 295 ≠ 0, we apply division lemma to 125 and 295, to get
295 = 125 x 2 + 45
Step 3: We consider the new divisor 125 and the new remainder 45, and apply the division lemma to get
125 = 45 x 2 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 295 and 420 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(125,45) = HCF(295,125) = HCF(420,295) .
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Frequently Asked Questions on HCF of 295, 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 295, 420?
Answer: HCF of 295, 420 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 295, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 295, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.