Highest Common Factor of 230, 302, 972, 406 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 230, 302, 972, 406 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 230, 302, 972, 406 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 230, 302, 972, 406 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 230, 302, 972, 406 is 2.
HCF(230, 302, 972, 406) = 2
HCF of 230, 302, 972, 406 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 230, 302, 972, 406 is 2.
Highest Common Factor of 230,302,972,406 is 2
Step 1: Since 302 > 230, we apply the division lemma to 302 and 230, to get
302 = 230 x 1 + 72
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 72 and 230, to get
230 = 72 x 3 + 14
Step 3: We consider the new divisor 72 and the new remainder 14, and apply the division lemma to get
72 = 14 x 5 + 2
We consider the new divisor 14 and the new remainder 2, and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 230 and 302 is 2
Notice that 2 = HCF(14,2) = HCF(72,14) = HCF(230,72) = HCF(302,230) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 2, we apply the division lemma to 972 and 2, to get
972 = 2 x 486 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 972 is 2
Notice that 2 = HCF(972,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 406 > 2, we apply the division lemma to 406 and 2, to get
406 = 2 x 203 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 406 is 2
Notice that 2 = HCF(406,2) .
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Frequently Asked Questions on HCF of 230, 302, 972, 406 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 230, 302, 972, 406?
Answer: HCF of 230, 302, 972, 406 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 230, 302, 972, 406 using Euclid's Algorithm?
Answer: For arbitrary numbers 230, 302, 972, 406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.