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 277, 700, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 277, 700, 107 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 277, 700, 107 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 277, 700, 107 is 1.
HCF(277, 700, 107) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 277, 700, 107 is 1.
Step 1: Since 700 > 277, we apply the division lemma to 700 and 277, to get
700 = 277 x 2 + 146
Step 2: Since the reminder 277 ≠ 0, we apply division lemma to 146 and 277, to get
277 = 146 x 1 + 131
Step 3: We consider the new divisor 146 and the new remainder 131, and apply the division lemma to get
146 = 131 x 1 + 15
We consider the new divisor 131 and the new remainder 15,and apply the division lemma to get
131 = 15 x 8 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 277 and 700 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(131,15) = HCF(146,131) = HCF(277,146) = HCF(700,277) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 1, we apply the division lemma to 107 and 1, to get
107 = 1 x 107 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 107 is 1
Notice that 1 = HCF(107,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 277, 700, 107?
Answer: HCF of 277, 700, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 277, 700, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 277, 700, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.