Highest Common Factor of 312, 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 312, 420 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 420 is 12 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 312, 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 312, 420 is 12.
HCF(312, 420) = 12
HCF of 312, 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 312, 420 is 12.
Highest Common Factor of 312,420 is 12
Step 1: Since 420 > 312, we apply the division lemma to 420 and 312, to get
420 = 312 x 1 + 108
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 108 and 312, to get
312 = 108 x 2 + 96
Step 3: We consider the new divisor 108 and the new remainder 96, and apply the division lemma to get
108 = 96 x 1 + 12
We consider the new divisor 96 and the new remainder 12, and apply the division lemma to get
96 = 12 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 312 and 420 is 12
Notice that 12 = HCF(96,12) = HCF(108,96) = HCF(312,108) = HCF(420,312) .
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Frequently Asked Questions on HCF of 312, 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 312, 420?
Answer: HCF of 312, 420 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.