Highest Common Factor of 77, 49, 63, 16 using Euclid's algorithm
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 77, 49, 63, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 77, 49, 63, 16 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 77, 49, 63, 16 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 77, 49, 63, 16 is 1.
HCF(77, 49, 63, 16) = 1
HCF of 77, 49, 63, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 77, 49, 63, 16 is 1.
Highest Common Factor of 77,49,63,16 is 1
Step 1: Since 77 > 49, we apply the division lemma to 77 and 49, to get
77 = 49 x 1 + 28
Step 2: Since the reminder 49 ≠ 0, we apply division lemma to 28 and 49, to get
49 = 28 x 1 + 21
Step 3: We consider the new divisor 28 and the new remainder 21, and apply the division lemma to get
28 = 21 x 1 + 7
We consider the new divisor 21 and the new remainder 7, and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 77 and 49 is 7
Notice that 7 = HCF(21,7) = HCF(28,21) = HCF(49,28) = HCF(77,49) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63 > 7, we apply the division lemma to 63 and 7, to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 63 is 7
Notice that 7 = HCF(63,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 7, we apply the division lemma to 16 and 7, to get
16 = 7 x 2 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: 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 7 and 16 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 77, 49, 63, 16 using Euclid's Algorithm
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 77, 49, 63, 16?
Answer: HCF of 77, 49, 63, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 77, 49, 63, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 77, 49, 63, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.