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 495, 770, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 495, 770, 714 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 495, 770, 714 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 495, 770, 714 is 1.
HCF(495, 770, 714) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 495, 770, 714 is 1.
Step 1: Since 770 > 495, we apply the division lemma to 770 and 495, to get
770 = 495 x 1 + 275
Step 2: Since the reminder 495 ≠ 0, we apply division lemma to 275 and 495, to get
495 = 275 x 1 + 220
Step 3: We consider the new divisor 275 and the new remainder 220, and apply the division lemma to get
275 = 220 x 1 + 55
We consider the new divisor 220 and the new remainder 55, and apply the division lemma to get
220 = 55 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 55, the HCF of 495 and 770 is 55
Notice that 55 = HCF(220,55) = HCF(275,220) = HCF(495,275) = HCF(770,495) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 714 > 55, we apply the division lemma to 714 and 55, to get
714 = 55 x 12 + 54
Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 54 and 55, to get
55 = 54 x 1 + 1
Step 3: We consider the new divisor 54 and the new remainder 1, and apply the division lemma to get
54 = 1 x 54 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 55 and 714 is 1
Notice that 1 = HCF(54,1) = HCF(55,54) = HCF(714,55) .
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 495, 770, 714?
Answer: HCF of 495, 770, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 495, 770, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 495, 770, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.