Highest Common Factor of 990, 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 990, 420 i.e. 30 the largest integer that leaves a remainder zero for all numbers.
HCF of 990, 420 is 30 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 990, 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 990, 420 is 30.
HCF(990, 420) = 30
HCF of 990, 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 990, 420 is 30.
Highest Common Factor of 990,420 is 30
Step 1: Since 990 > 420, we apply the division lemma to 990 and 420, to get
990 = 420 x 2 + 150
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 150 and 420, to get
420 = 150 x 2 + 120
Step 3: We consider the new divisor 150 and the new remainder 120, and apply the division lemma to get
150 = 120 x 1 + 30
We consider the new divisor 120 and the new remainder 30, and apply the division lemma to get
120 = 30 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 990 and 420 is 30
Notice that 30 = HCF(120,30) = HCF(150,120) = HCF(420,150) = HCF(990,420) .
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Frequently Asked Questions on HCF of 990, 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 990, 420?
Answer: HCF of 990, 420 is 30 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 990, 420 using Euclid's Algorithm?
Answer: For arbitrary numbers 990, 420 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.