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 945, 266, 270 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 266, 270 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 945, 266, 270 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 945, 266, 270 is 1.
HCF(945, 266, 270) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 266, 270 is 1.
Step 1: Since 945 > 266, we apply the division lemma to 945 and 266, to get
945 = 266 x 3 + 147
Step 2: Since the reminder 266 ≠ 0, we apply division lemma to 147 and 266, to get
266 = 147 x 1 + 119
Step 3: We consider the new divisor 147 and the new remainder 119, and apply the division lemma to get
147 = 119 x 1 + 28
We consider the new divisor 119 and the new remainder 28,and apply the division lemma to get
119 = 28 x 4 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 945 and 266 is 7
Notice that 7 = HCF(28,7) = HCF(119,28) = HCF(147,119) = HCF(266,147) = HCF(945,266) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 7, we apply the division lemma to 270 and 7, to get
270 = 7 x 38 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 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 7 and 270 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(270,7) .
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 945, 266, 270?
Answer: HCF of 945, 266, 270 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 266, 270 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 266, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.