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 3478, 1042, 68953 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3478, 1042, 68953 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 3478, 1042, 68953 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 3478, 1042, 68953 is 1.
HCF(3478, 1042, 68953) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3478, 1042, 68953 is 1.
Step 1: Since 3478 > 1042, we apply the division lemma to 3478 and 1042, to get
3478 = 1042 x 3 + 352
Step 2: Since the reminder 1042 ≠ 0, we apply division lemma to 352 and 1042, to get
1042 = 352 x 2 + 338
Step 3: We consider the new divisor 352 and the new remainder 338, and apply the division lemma to get
352 = 338 x 1 + 14
We consider the new divisor 338 and the new remainder 14,and apply the division lemma to get
338 = 14 x 24 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 3478 and 1042 is 2
Notice that 2 = HCF(14,2) = HCF(338,14) = HCF(352,338) = HCF(1042,352) = HCF(3478,1042) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68953 > 2, we apply the division lemma to 68953 and 2, to get
68953 = 2 x 34476 + 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 68953 is 1
Notice that 1 = HCF(2,1) = HCF(68953,2) .
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 3478, 1042, 68953?
Answer: HCF of 3478, 1042, 68953 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3478, 1042, 68953 using Euclid's Algorithm?
Answer: For arbitrary numbers 3478, 1042, 68953 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.