Highest Common Factor of 420, 1545 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 420, 1545 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 1545 is 15 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 420, 1545 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 420, 1545 is 15.
HCF(420, 1545) = 15
HCF of 420, 1545 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 1545 is 15.
Highest Common Factor of 420,1545 is 15
Step 1: Since 1545 > 420, we apply the division lemma to 1545 and 420, to get
1545 = 420 x 3 + 285
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 285 and 420, to get
420 = 285 x 1 + 135
Step 3: We consider the new divisor 285 and the new remainder 135, and apply the division lemma to get
285 = 135 x 2 + 15
We consider the new divisor 135 and the new remainder 15, and apply the division lemma to get
135 = 15 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 420 and 1545 is 15
Notice that 15 = HCF(135,15) = HCF(285,135) = HCF(420,285) = HCF(1545,420) .
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Frequently Asked Questions on HCF of 420, 1545 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 420, 1545?
Answer: HCF of 420, 1545 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 1545 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 1545 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.