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 747, 477, 999 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 747, 477, 999 is 9 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 747, 477, 999 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 747, 477, 999 is 9.
HCF(747, 477, 999) = 9
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 747, 477, 999 is 9.
Step 1: Since 747 > 477, we apply the division lemma to 747 and 477, to get
747 = 477 x 1 + 270
Step 2: Since the reminder 477 ≠ 0, we apply division lemma to 270 and 477, to get
477 = 270 x 1 + 207
Step 3: We consider the new divisor 270 and the new remainder 207, and apply the division lemma to get
270 = 207 x 1 + 63
We consider the new divisor 207 and the new remainder 63,and apply the division lemma to get
207 = 63 x 3 + 18
We consider the new divisor 63 and the new remainder 18,and apply the division lemma to get
63 = 18 x 3 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 747 and 477 is 9
Notice that 9 = HCF(18,9) = HCF(63,18) = HCF(207,63) = HCF(270,207) = HCF(477,270) = HCF(747,477) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 999 > 9, we apply the division lemma to 999 and 9, to get
999 = 9 x 111 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 999 is 9
Notice that 9 = HCF(999,9) .
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 747, 477, 999?
Answer: HCF of 747, 477, 999 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 747, 477, 999 using Euclid's Algorithm?
Answer: For arbitrary numbers 747, 477, 999 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.