Highest Common Factor of 278, 661, 10 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 278, 661, 10 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 661, 10 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 278, 661, 10 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 278, 661, 10 is 1.
HCF(278, 661, 10) = 1
HCF of 278, 661, 10 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 278, 661, 10 is 1.
Highest Common Factor of 278,661,10 is 1
Step 1: Since 661 > 278, we apply the division lemma to 661 and 278, to get
661 = 278 x 2 + 105
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 105 and 278, to get
278 = 105 x 2 + 68
Step 3: We consider the new divisor 105 and the new remainder 68, and apply the division lemma to get
105 = 68 x 1 + 37
We consider the new divisor 68 and the new remainder 37,and apply the division lemma to get
68 = 37 x 1 + 31
We consider the new divisor 37 and the new remainder 31,and apply the division lemma to get
37 = 31 x 1 + 6
We consider the new divisor 31 and the new remainder 6,and apply the division lemma to get
31 = 6 x 5 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 278 and 661 is 1
Notice that 1 = HCF(6,1) = HCF(31,6) = HCF(37,31) = HCF(68,37) = HCF(105,68) = HCF(278,105) = HCF(661,278) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
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Frequently Asked Questions on HCF of 278, 661, 10 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 278, 661, 10?
Answer: HCF of 278, 661, 10 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 661, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 661, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.