Highest Common Factor of 445, 278 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 445, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 445, 278 is 1 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 445, 278 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 445, 278 is 1.
HCF(445, 278) = 1
HCF of 445, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 445, 278 is 1.
Highest Common Factor of 445,278 is 1
Step 1: Since 445 > 278, we apply the division lemma to 445 and 278, to get
445 = 278 x 1 + 167
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 167 and 278, to get
278 = 167 x 1 + 111
Step 3: We consider the new divisor 167 and the new remainder 111, and apply the division lemma to get
167 = 111 x 1 + 56
We consider the new divisor 111 and the new remainder 56,and apply the division lemma to get
111 = 56 x 1 + 55
We consider the new divisor 56 and the new remainder 55,and apply the division lemma to get
56 = 55 x 1 + 1
We consider the new divisor 55 and the new remainder 1,and apply the division lemma to get
55 = 1 x 55 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 445 and 278 is 1
Notice that 1 = HCF(55,1) = HCF(56,55) = HCF(111,56) = HCF(167,111) = HCF(278,167) = HCF(445,278) .
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Frequently Asked Questions on HCF of 445, 278 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 445, 278?
Answer: HCF of 445, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 445, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 445, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.