Highest Common Factor of 308, 442 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 308, 442 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 308, 442 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 308, 442 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 308, 442 is 2.
HCF(308, 442) = 2
HCF of 308, 442 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 308, 442 is 2.
Highest Common Factor of 308,442 is 2
Step 1: Since 442 > 308, we apply the division lemma to 442 and 308, to get
442 = 308 x 1 + 134
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 134 and 308, to get
308 = 134 x 2 + 40
Step 3: We consider the new divisor 134 and the new remainder 40, and apply the division lemma to get
134 = 40 x 3 + 14
We consider the new divisor 40 and the new remainder 14,and apply the division lemma to get
40 = 14 x 2 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 308 and 442 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(134,40) = HCF(308,134) = HCF(442,308) .
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Frequently Asked Questions on HCF of 308, 442 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 308, 442?
Answer: HCF of 308, 442 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 308, 442 using Euclid's Algorithm?
Answer: For arbitrary numbers 308, 442 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.