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 741, 429, 856 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 429, 856 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 741, 429, 856 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 741, 429, 856 is 1.
HCF(741, 429, 856) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 741, 429, 856 is 1.
Step 1: Since 741 > 429, we apply the division lemma to 741 and 429, to get
741 = 429 x 1 + 312
Step 2: Since the reminder 429 ≠ 0, we apply division lemma to 312 and 429, to get
429 = 312 x 1 + 117
Step 3: We consider the new divisor 312 and the new remainder 117, and apply the division lemma to get
312 = 117 x 2 + 78
We consider the new divisor 117 and the new remainder 78,and apply the division lemma to get
117 = 78 x 1 + 39
We consider the new divisor 78 and the new remainder 39,and apply the division lemma to get
78 = 39 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 39, the HCF of 741 and 429 is 39
Notice that 39 = HCF(78,39) = HCF(117,78) = HCF(312,117) = HCF(429,312) = HCF(741,429) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 856 > 39, we apply the division lemma to 856 and 39, to get
856 = 39 x 21 + 37
Step 2: Since the reminder 39 ≠ 0, we apply division lemma to 37 and 39, to get
39 = 37 x 1 + 2
Step 3: We consider the new divisor 37 and the new remainder 2, and apply the division lemma to get
37 = 2 x 18 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 39 and 856 is 1
Notice that 1 = HCF(2,1) = HCF(37,2) = HCF(39,37) = HCF(856,39) .
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 741, 429, 856?
Answer: HCF of 741, 429, 856 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 429, 856 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 429, 856 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.