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 448, 734, 761 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 734, 761 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 448, 734, 761 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 448, 734, 761 is 1.
HCF(448, 734, 761) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 734, 761 is 1.
Step 1: Since 734 > 448, we apply the division lemma to 734 and 448, to get
734 = 448 x 1 + 286
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 286 and 448, to get
448 = 286 x 1 + 162
Step 3: We consider the new divisor 286 and the new remainder 162, and apply the division lemma to get
286 = 162 x 1 + 124
We consider the new divisor 162 and the new remainder 124,and apply the division lemma to get
162 = 124 x 1 + 38
We consider the new divisor 124 and the new remainder 38,and apply the division lemma to get
124 = 38 x 3 + 10
We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get
38 = 10 x 3 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 448 and 734 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(124,38) = HCF(162,124) = HCF(286,162) = HCF(448,286) = HCF(734,448) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 761 > 2, we apply the division lemma to 761 and 2, to get
761 = 2 x 380 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 761 is 1
Notice that 1 = HCF(2,1) = HCF(761,2) .
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 448, 734, 761?
Answer: HCF of 448, 734, 761 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 734, 761 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 734, 761 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.